What Is the Magnetic Force?

Short answer

• Magnetic force is the push or pull that a magnetic field exerts on a moving electric charge or on a wire carrying an electric current. A charge that is standing still in a magnetic field feels no magnetic force at all.
• The force is always at a right angle to both the motion of the charge and the direction of the magnetic field. That right angle rule is what makes the force steer a moving charge into a curve instead of speeding it up or slowing it down.
• The size of the force on a single charge follows the Lorentz force law, F = qvB sin(theta), where q is the charge, v is its speed, B is the strength of the magnetic field, and theta is the angle between the motion and the field. The force is largest when the charge moves at a right angle to the field and zero when it moves parallel to the field.
• The magnetic force on a charge is not the same thing as the force between two magnets. The two are related, because both come from magnetic fields, but the force on a charge follows the rules in this article, while the attraction between two magnets is the force between two magnetic dipoles.
• You meet magnetic force every day in electric motors, generators, compasses, loudspeakers, and MRI scanners, and in nature in the aurora and in the paths of charged particles in space.

What Magnetic Force Is, in Plain Language

Magnetic force is the force that a magnetic field exerts on something that carries electric charge and is moving. The two conditions matter equally. The charge must be moving, and there must be a magnetic field for it to move through. Take either one away and the magnetic force disappears.

A useful way to picture it is to think of a magnetic field as a set of invisible lines filling the space around a magnet or around a wire that carries a current. A charged particle, such as an electron or a proton, travels through that space. As long as it moves, the field pushes on it sideways. The push is not along the direction the particle is already traveling, and it is not along the direction of the field lines either. It is sideways to both, and that sideways push is the magnetic force.

Encyclopaedia Britannica defines magnetic force as the attraction or repulsion that arises between electrically charged particles because of their motion, and notes that it is the basic force behind effects such as the action of electric motors and the attraction of magnets for iron. The definition points to the central fact about this force: motion is what brings it into being. Electric forces exist among stationary electric charges, but both electric and magnetic forces exist among moving electric charges. A charge sitting still feels an electric force from another charge, but it feels no magnetic force until it starts to move.

That single rule clears up many common confusions. A charged balloon stuck to a wall is held there by electric force, not magnetic force, because nothing is moving. A compass needle turns because the needle itself is a small magnet sitting in the magnetic field of the Earth, which is a different arrangement from a single charge moving through a field. Both are magnetism, but the force on a moving charge is the specific idea this article explains, and the force between magnets is covered separately below so the two are not mixed up.

The magnetic force is also one part of a larger picture. Magnetic fields and electric fields are related, and together they make up the electromagnetic force. The Georgia Institute of Technology Physics Book notes that the electromagnetic force is the second strongest of the four fundamental forces, behind the strong nuclear force and ahead of the weak force and the gravitational force. Our guide to the force of gravity explains the weakest of the four, and the contrast is instructive: gravity pulls on mass, while the magnetic force pushes on moving charge.

The One Rule That Explains Most of It: Only Moving Charges Feel It

If you remember one sentence from this article, make it this one: a magnetic field exerts no force on a stationary charge. The charge has to be moving relative to the field before anything happens.

HyperPhysics, the physics reference from Georgia State University, states the point directly among the implications of the Lorentz force law: the magnetic force on a stationary charge, or on a charge moving parallel to the magnetic field, is zero. The Georgia Tech Physics Book makes the same point in plain terms: any particle at rest will not experience any magnetic force.

The rule also works in the other direction. The faster a charge moves through a field, the stronger the push, as long as the direction of motion stays the same. Double the speed and the force doubles. Double the charge and the force doubles. Double the strength of the field and the force doubles. The force is proportional to all three, which is why the formula multiplies them together.

There is one more condition, and it is easy to overlook. The force also depends on the angle between the motion and the field. A charge moving exactly along the field lines, parallel to them, feels no force at all, even though it is moving fast. A charge moving exactly across the field lines, at a right angle to them, feels the maximum force. At angles in between, the force falls somewhere between zero and the maximum. The sine of the angle in the formula is what captures that smooth change from zero to maximum and back again.

This angle dependence is not a small detail. It is the reason the force can steer a particle without ever changing its speed, and it is the reason a current carrying wire can be pushed sideways in a motor. Both effects follow from the same geometry, and both are explained in the sections below.

What a Magnetic Field Is

A magnetic force needs a magnetic field to act through, so it helps to say what a magnetic field is before going further. A magnetic field is a region of space in which a moving charge or a magnet experiences a magnetic force. Physicists describe it with the symbol B, and they measure its strength in a unit called the tesla.

The field is a vector field, which means that at every point in space it has both a strength and a direction. The Georgia Tech Physics Book describes it exactly that way: the magnetic field extends in all three dimensions, and it has a direction as well as a magnitude at each point. You can picture the direction with field lines, the curves that run out of the north pole of a magnet and back into its south pole. A compass needle lines up along those lines, and a moving charge feels its push at a right angle to them.

Magnetic fields are produced most simply by moving charges or by magnetic dipoles, which are the tiny north and south pole pairs found in magnets. An electric current is a flow of moving charges, so every wire carrying a current is surrounded by a magnetic field. That is why an electric current can push on a nearby magnet, and why two wires carrying currents can push on each other. The field is the go between: one moving charge creates a field, and that field exerts a force on another moving charge.

The strength of the field matters a great deal, because the force on a charge is proportional to it. The tesla is a large unit, so everyday fields are usually described in smaller units. HyperPhysics notes that one tesla equals 10,000 gauss, and that the magnetic field of the Earth at the surface is on the order of half a gauss. The University of California, Santa Barbara, puts the range more precisely: the field at the surface of the Earth runs from about 0.25 gauss to 0.65 gauss, depending on location, because the field is stronger near the magnetic poles and weaker near the magnetic equator. In the smaller SI unit, that range is about 25 to 65 microtesla, since one gauss equals 100 microtesla. A small neodymium supermagnet, by comparison, can generate a field of thousands of gauss close to its surface, according to the University of California, Santa Barbara, so even a magnet that fits on a fingertip is far stronger than the field of the whole Earth at the point where you hold it. The difference is that the field of the Earth fills an enormous volume of space, while the field of a small magnet fades within a few inches.

For the wider context of fields that fill space around the Earth, see Earth’s electromagnetic field. For the waves that travel through the electromagnetic field, see What Is the Electromagnetic Spectrum?

The Lorentz Force, Explained in Plain Language

The law that describes the magnetic force on a moving charge is called the Lorentz force law. It is named in every standard physics reference, and HyperPhysics defines the magnetic field itself from it, which shows how central it is. The law has two parts, one electric and one magnetic, and the full version covers a charge sitting in both an electric field and a magnetic field at the same time.

The full Lorentz force law is F = q(E + v x B). In that expression, F is the total force on the charge, q is the charge, E is the electric field, v is the velocity of the charge, and B is the magnetic field. The symbol x between v and B stands for a cross product, which is a mathematical way of saying that the result points at a right angle to both v and B. The electric part, qE, is the ordinary electric force: it pushes a positive charge along the direction of the electric field. The magnetic part, q(v x B), is the magnetic force, and it is the part this article is about.

When there is no electric field, or when you want to look at the magnetic part on its own, the law simplifies to F = q(v x B). Written in terms of size alone, it becomes F = qvB sin(theta), where theta is the angle between the velocity and the magnetic field. Each symbol in that short formula carries one piece of the story:

• q, the charge, measured in coulombs. A bigger charge feels a bigger force. A negative charge, such as an electron, feels a force in the opposite direction to a positive charge moving the same way.
• v, the speed of the charge, measured in meters per second. A charge at rest has v equal to zero, so the force is zero. A faster charge feels a stronger force.
• B, the strength of the magnetic field, measured in tesla. A stronger field pushes harder.
• sin(theta), the sine of the angle between the motion and the field. When the motion is at a right angle to the field, theta is 90 degrees and sin(theta) is 1, so the force is at its maximum. When the motion is parallel to the field, theta is 0 degrees and sin(theta) is 0, so the force is zero.

The direction of the force is as important as its size. The cross product means the force is perpendicular to both the velocity and the field. If the velocity points east and the field points north, the force points up or down, not east or north. Which of the two it is depends on the sign of the charge and on the right-hand rule, which is explained in the next section.

One consequence of that perpendicular direction deserves emphasis, because it surprises most readers. A magnetic force can change the direction of a moving charge, but it cannot change its speed. The reason is that the force always acts sideways to the motion, never along it, so it never adds energy to the charge or takes energy away from it. Physicists say that the magnetic force does no work on a moving charge. A charge curving through a magnetic field keeps exactly the speed it had when it entered, and it leaves with the same speed, traveling in a new direction.

The Right-Hand Rule and the Direction of the Force

The right-hand rule is the practical tool for finding the direction of the magnetic force. It turns the cross product into something you can do with your own hand, and it is worth learning properly, because the direction is half of the answer in any magnetic force problem.

For a positive charge, hold your right hand flat with your fingers pointing in the direction of the velocity, then curl your fingers toward the direction of the magnetic field. Your thumb points in the direction of the magnetic force. Another version of the same rule uses three fingers: point the fingers of your right hand along the velocity, point your middle finger along the field, and your thumb gives the force. Different textbooks present the hand position slightly differently, but the geometry is the same in every version: velocity, field, and force are all at right angles to one another, like the three edges that meet at the corner of a box.

For a negative charge, such as an electron, the force points in exactly the opposite direction. Find the direction for a positive charge first, then reverse it. Forgetting that reversal is the most common mistake in magnetic force problems, and it is worth checking the sign of the charge before doing anything else.

A simple example makes the rule concrete. Imagine a proton moving to the right across the page, while the magnetic field points straight out of the page toward you. Point your right hand fingers to the right, curl them toward yourself, and your thumb points upward. The proton is pushed upward. If the particle were an electron moving the same way through the same field, the push would be downward instead. The size of the push would be the same; only the direction would reverse.

The right-hand rule also explains why the force is zero when the motion is parallel to the field. If your fingers already point along the field, there is nothing to curl toward, and no perpendicular direction is defined. The cross product of two parallel vectors is zero, which is the mathematical form of the same fact.

Why the Force Bends Paths Into Circles

Because the magnetic force is always perpendicular to the motion, it acts as a steering force. It never speeds a charge up or slows it down, but it constantly changes the direction of travel. When the field is uniform and the charge moves at a right angle to it, that constant sideways push bends the path into a circle.

The picture is easiest to see step by step. A charged particle enters a uniform magnetic field moving in a straight line. The field pushes it sideways, so its direction changes slightly. Now it is moving in a slightly different direction, but the force is still perpendicular to the new direction, so it pushes sideways again. The push keeps turning with the particle, always at a right angle to the motion, and the result is a circular path. The particle goes around and around the circle at the same speed it had when it entered.

The radius of that circle follows a simple formula, r = mv/(qB), where m is the mass of the particle, v is its speed, q is its charge, and B is the strength of the field. The formula makes intuitive sense once it is read in parts. A heavier particle is harder to turn, so it travels in a wider circle. A faster particle also travels in a wider circle, because it covers more distance before the sideways push can turn it. A larger charge feels a stronger push, so it turns more sharply, in a smaller circle. A stronger field pushes harder, so it also makes a smaller circle.

The connection to circular motion is not a coincidence. A force that always points toward the center of a circle is a centripetal force, and the magnetic force plays exactly that role here. Our guide to what centripetal force is explains the general idea: any force that keeps an object moving in a circle by pulling it toward the center. In a magnetic field, the magnetic force does that job for a charged particle, which is why the same mathematics appears in both places.

If the charge also has some motion along the direction of the field, the path becomes a helix, a spiral like a stretched spring. The part of the motion across the field goes around in a circle, while the part along the field continues in a straight line, and the combination traces a corkscrew. Charged particles trapped in the magnetic field of the Earth travel in just this kind of spiral, and when they strike the upper atmosphere near the poles they produce the aurora. For the aurora itself, including where and when it appears, see Northern Lights Aurora Borealis Alaska.

The Magnetic Force on a Current Carrying Wire

A wire carrying an electric current is a stream of moving charges, so it feels a magnetic force for the same reason a single charge does. The current is simply many charges moving together, and the force on each one adds up to a force on the whole wire. That is the principle behind every electric motor.

For a straight wire of length L carrying a current I in a uniform magnetic field B, the force is F = ILB sin(theta), where theta is the angle between the wire and the field. The direction follows the same right-hand rule, with the direction of the current taking the place of the velocity of a single charge. Point your fingers along the current, curl them toward the field, and your thumb gives the direction of the force on the wire.

The Georgia Tech Physics Book works through an example that shows the size of the effect. A wire carries a current of 6 amps and sits in a constant magnetic field of 1 tesla. The wire is 6 centimeters long, which is 0.06 meters. The field points out of the page and the current runs upward, so the angle between them is 90 degrees and sin(theta) is 1. The force is F = (6 amps) x (0.06 meters) x (1 tesla) = 0.36 newtons. The direction, by the right-hand rule, is to the right. A force of 0.36 newtons is small, about the weight of a small apple slice, but it is a real push, and in a motor many turns of wire and a stronger field multiply it into a useful turning force.

The wire version of the law also explains why two wires carrying currents can attract or repel each other. Each wire creates a magnetic field around itself, and the other wire, carrying moving charges, feels a force in that field. When the currents run in the same direction, the wires attract each other. When the currents run in opposite directions, they repel. The force between the wires is a magnetic force acting on moving charges, with the field of one wire doing the pushing on the charges in the other.

Magnetic Force Compared With Electric Force

Readers often mix up magnetic force and electric force, which is understandable, because both act on charges and both are parts of the electromagnetic force. The table below sets out the differences plainly.

The most important row is the first one. An electric field pushes on a charge whether it moves or not. A magnetic field waits for motion. That is why a charged particle sitting still in a magnetic field can be completely unaffected, while the same particle in an electric field would be pushed at once.

The two forces also differ in what they do to energy. An electric force can do work on a charge, giving it kinetic energy or taking it away, which is how a charge speeds up as it falls through a voltage. A magnetic force, acting always sideways to the motion, cannot do work on a single charge, so it cannot change the speed. It can only redirect the charge. In a motor, the situation looks different at first glance, because a motor clearly does work, but the work there is done by the electric field driving the current and by the changing magnetic fields, not by the magnetic force on a charge acting alone.

The Force Between Two Magnets Is a Different Arrangement

The gate rule for this article is to keep two ideas distinct: the magnetic force on a moving charge, and the force between two magnets. They are related, but they are not the same arrangement, and treating them as one causes confusion.

When two bar magnets are brought near each other, opposite poles attract and like poles repel. A north pole and a south pole pull together; two north poles push apart. Britannica gives the attraction of magnets for iron as one of the basic effects of magnetic force, and the pole rule is the everyday form of that effect. The reason it happens is that each magnet is a magnetic dipole, a north pole and a south pole bound together, and each dipole sits in the magnetic field created by the other. The field exerts forces on the two poles in opposite directions, and because the field is stronger near one pole than the other, the pushes do not cancel, leaving a net attraction or repulsion and a turning effect that lines the magnets up.

That is a different picture from a single charge moving through a field. A charge has no poles and no north or south end. It feels a force only while it moves, and the force is sideways to its motion. A bar magnet feels a force while sitting still, because its poles are already sitting in the other magnet’s field. The two situations share the same underlying physics, because the magnetism of a bar magnet itself comes from the motion and alignment of charges inside the material, but the force you observe in each case follows different rules.

The distinction also matters for what magnets attract. A magnet does not attract every metal. It attracts ferromagnetic materials, principally iron, nickel, and cobalt, and alloys made from them, such as steel. It does not attract copper, aluminum, gold, wood, plastic, or glass in any noticeable way. The reason is that in a ferromagnetic material the tiny magnetic dipoles of the atoms can line up with an applied field, strengthening it, while in other materials they cannot. A refrigerator magnet sticks to a steel fridge door because the steel is ferromagnetic; it will not stick to an aluminum pan, because aluminum is not.

A compass is a small magnet, not a moving charge, and it works by the dipole rule. Its needle is magnetized so that one end is a north seeking pole, and the magnetic field of the Earth exerts a turning force on it until it lines up with the field. The needle points north because the field of the Earth runs roughly from its southern magnetic pole to its northern magnetic pole. No charge needs to move through the needle for it to turn, which is exactly the difference between the two arrangements.

Where Magnetic Fields Come From

Magnetic fields have three main sources, and each one is a version of the same underlying fact: moving charge creates a magnetic field.

The first source is an electric current. When charges flow through a wire, they create a magnetic field that circles the wire. The Danish physicist Hans Christian Oersted demonstrated this in 1820, when he showed that a current carrying wire could deflect a compass needle. The Georgia Tech Physics Book records that discovery and its consequence: it was realized that magnetic fields radiate from all sides of a wire carrying an electric current, providing proof that electricity and magnetism were interrelated. Before Oersted, electricity and magnetism were thought to be separate forces. After him, they were understood as two faces of one force, and the Scottish physicist James Clerk Maxwell later gave that unity its mathematical form in his Treatise on Electricity and Magnetism.

The second source is a permanent magnet. Inside a piece of iron, each atom carries a tiny magnetic field of its own, produced by the motion and spin of its electrons. In an unmagnetized piece of iron, those tiny fields point in random directions and cancel each other out. In a magnet, large regions of atoms have their fields lined up in the same direction, and their fields add together into a strong field that reaches outside the material. Heating a magnet or striking it hard can disturb that alignment and weaken it, which is why a magnet can lose its strength.

The third source is a changing electric field. Maxwell’s work showed that a changing electric field creates a magnetic field, just as a changing magnetic field creates an electric field. That mutual creation is what allows electromagnetic waves, including light, to travel through empty space. It is also the reason the electromagnetic spectrum exists as a single family of waves. For that family, from radio waves to gamma rays, see What Is the Electromagnetic Spectrum?

The field of the Earth is a large scale example of the first source. It is generated by flowing currents of molten iron in the outer core of the planet, a natural dynamo on an enormous scale. The University of California, Santa Barbara, describes it as generated by flowing currents of molten iron in the outer shell of the core, and notes that the resulting field at the surface is weak, only 0.25 gauss to 0.65 gauss, but very large in space, because the core is so massive. That weak, planet sized field is what turns compasses, guides migrating animals, and shields the atmosphere by deflecting many of the charged particles streaming from the Sun.

Units: Newtons, Tesla, and Gauss

Three units appear in almost every discussion of magnetic force, and keeping them straight removes a lot of confusion.

The newton, symbol N, is the unit of force, and it is the unit of magnetic force just as it is the unit of every other force. When the Lorentz force law gives a result in newtons, it is giving the same kind of quantity as the weight of an object or the push of a hand.

The tesla, symbol T, is the SI unit of magnetic field strength, properly called magnetic flux density. It is a large unit. One tesla is the field in which a charge of one coulomb moving at one meter per second at a right angle to the field feels a force of one newton. That definition comes straight from the Lorentz force law: set q to 1, v to 1, and sin(theta) to 1, and F equals B. HyperPhysics gives the same relationship in terms of the wire formula, noting that the units of magnetic field are newtons per ampere meter, and that this unit is named the tesla.

The gauss, symbol G, is an older unit of magnetic field strength that is still widely used, especially for small fields. One tesla equals 10,000 gauss, so one gauss equals 0.0001 tesla. The field of the Earth, at about 0.5 gauss, is about 0.00005 tesla, which is 50 microtesla. A microtesla is one millionth of a tesla, and it is the convenient unit for fields as weak as the Earth’s.

A common mistake is to confuse the unit of the field with the unit of the force. The tesla measures the field, the newton measures the force the field exerts. A strong field does not by itself guarantee a strong force: a still charge in a field of a thousand tesla would feel nothing, while a fast, highly charged particle in a weak field can feel a measurable push.

Worked Examples

Two worked examples, both taken from the Georgia Tech Physics Book and checked against the Lorentz force law, show how the formula is used in practice. The numbers are the source’s own, so the arithmetic can be followed step by step.

Example 1: A single charge in a magnetic field

A charge of 1 coulomb moves at 3 meters per second. Its velocity makes an angle of 60 degrees with a magnetic field of 2 tesla. What is the magnitude of the force on the charge?

The formula is F = qvB sin(theta). Substituting the values gives F = (1 coulomb) x (3 meters per second) x (2 tesla) x sin(60 degrees). The sine of 60 degrees is about 0.866. Multiplying through gives F = 1 x 3 x 2 x 0.866 = 5.196 newtons. The direction of the force is at a right angle to both the velocity and the field, found with the right-hand rule, and it reverses if the charge is negative.

Example 2: A current carrying wire in a magnetic field

A wire carries a current of 6 amps in a constant magnetic field of 1 tesla. The wire is 6 centimeters long, which is 0.06 meters, and the field points out of the page while the current runs upward, so the angle between them is 90 degrees.

The formula is F = ILB sin(theta). Substituting gives F = (6 amps) x (0.06 meters) x (1 tesla) x sin(90 degrees). The sine of 90 degrees is 1, so F = 6 x 0.06 x 1 = 0.36 newtons. The direction, by the right-hand rule, is to the right, in the positive x direction. The example shows how modest the force on a single short wire can be, and why motors use many turns of wire in strong fields to build up a useful turning force.

Where Magnetic Force Does Useful Work

Magnetic force is not an abstract idea confined to textbooks. It is the working principle of much of modern technology, and the examples below all follow from the rules already covered.

Electric motors are the most direct application. A motor is a set of coils of wire carrying current inside a magnetic field. The field exerts a force on each side of each coil, and because the current runs in opposite directions on the two sides, the forces point in opposite directions and turn the coil. A commutator reverses the current at the right moment on each half turn, so the turning continues in the same direction instead of rocking back and forth. Every fan, washing machine, electric car, and power tool contains a motor working on this principle.

Generators are motors run in reverse. Instead of using a current to make a coil turn, a generator turns a coil inside a magnetic field, and the changing field induces a current in the wire. The University of California, Santa Barbara, notes the symmetry plainly: a generator and a permanent magnet motor are basically the same thing, and spinning the shaft of a motor produces a voltage at its terminals. Power stations use this principle at an enormous scale, turning turbines with steam, water, or wind and converting that rotation into electricity through magnetic force and induction.

MRI scanners use magnetic fields in a different way. The Georgia Tech Physics Book notes that the magnetic force is connected directly to magnetic resonance imaging, through which doctors can learn a great deal about the condition of the human body, including tracking tumors and diagnosing injuries and diseases. An MRI scanner uses a very strong magnetic field, several tesla in strength, to align the magnetic moments of hydrogen nuclei in the body, then uses radio waves to disturb them and listens to the signals they give off as they settle back. The image is built from those signals. The strength of the field is part of why an MRI scanner is a large, expensive machine, and why metal objects must be kept out of the room.

Particle accelerators use magnetic force as a steering system. In a cyclotron, an electric field accelerates charged particles while a magnetic field bends their paths into spirals, so they pass through the accelerating field again and again and gain energy on each pass. In the large circular accelerators used in research, magnets around the ring keep the particle beam on its circular path, bending it a little at each magnet. Without magnetic force, there would be no way to hold a beam of fast particles on a curved track.

Loudspeakers use the force on a wire in a simpler form. A coil of wire attached to a cone sits in the field of a permanent magnet. When an audio signal drives a varying current through the coil, the magnetic force on the coil varies with it, pushing the cone back and forth and producing sound waves in the air. The cone moves exactly as the current dictates, which is why a loudspeaker can reproduce music and speech.

Compasses and navigation use the dipole side of magnetism, the force on a magnet rather than on a moving charge, but they depend on the same planetary field. The field of the Earth is weak, yet it is steady and it covers the whole planet, so a freely turning magnetized needle lines up with it anywhere on Earth. Animals such as migratory birds are believed to sense the field as well, although the mechanism is still a subject of research and is not settled science.

The aurora is nature’s own display of magnetic force. Charged particles from the Sun are caught by the magnetic field of the Earth and guided along its field lines toward the poles, where they spiral down and collide with atoms in the upper atmosphere. Those collisions release light, producing the moving curtains of the northern and southern lights. The particles follow helical paths because the magnetic force bends their motion across the field while their motion along the field continues, exactly the spiral described earlier in this article.

Common Misunderstandings

Several misunderstandings about magnetic force appear again and again, and each one is corrected by a rule already stated in this article.

The first is the idea that magnets attract all metals. They do not. They attract ferromagnetic materials, principally iron, nickel, and cobalt, and alloys such as steel. A magnet will not pick up a copper coin or an aluminum can. If a metal object sticks to a magnet, that is evidence that it contains a ferromagnetic material, not that all metals behave that way.

The second is the idea that a magnetic field can speed up a charged particle. It cannot. The force is always perpendicular to the motion, so it changes direction only. A particle accelerator needs electric fields to add energy and speed; the magnets are there to steer, not to accelerate.

The third is the idea that a stationary charge feels a magnetic force. It does not. This is the most important rule in the article, and it is also the most commonly forgotten. A charge must be moving relative to the field. The same applies to a wire: no current, no magnetic force on the wire.

The fourth is the idea that magnetic poles can be separated. Cutting a bar magnet in half does not produce a separate north pole and a separate south pole. Each half becomes a complete magnet with its own north and south pole. As far as physics has established, isolated magnetic poles, called magnetic monopoles, do not exist in ordinary matter, although some theories predict them. This is a statement about what has been observed, and the article does not claim that monopoles are impossible in principle.

The fifth is the idea that magnetic force is a separate force from electric force in some absolute sense. The two are parts of one electromagnetic force, and whether a given effect looks electric or magnetic can depend on the frame of reference of the observer. A charge that is still in one frame is moving in another, so the balance between the electric and magnetic parts shifts. That is a deeper point than this article needs to develop, but it is the reason physicists speak of the electromagnetic force as one force with two aspects, rather than two unrelated forces.

The sixth is the idea that a bigger magnet is always a stronger magnet. Size and strength are different things. A small magnet made of neodymium iron boride can produce a field of thousands of gauss close to its surface, far stronger than the field of a large but weakly magnetized piece of iron. What a large magnet has is reach: its field extends over a larger volume, even if it is weak at any one point. The field of the Earth is the extreme case of this trade off, very weak but planet sized.

A Short History

Electricity and magnetism were thought to be separate forces until the nineteenth century. The turning point came in 1820, when Hans Christian Oersted showed that an electric current could deflect a compass needle, proving that a current creates a magnetic field. The Georgia Tech Physics Book records that a Danish physicist realized in 1820 that the magnetic field from a circuit could be turned on and off with the circuit, and that this was when it was realized that magnetic fields radiate from all sides of a wire carrying an electric current.

James Clerk Maxwell then brought electricity and magnetism together in a single mathematical theory, published in his Treatise on Electricity and Magnetism. His equations showed that a changing electric field creates a magnetic field and a changing magnetic field creates an electric field, and that the two together travel as waves at the speed of light. Light itself turned out to be an electromagnetic wave, which is why the study of magnetic force leads directly to the study of light and the electromagnetic spectrum.

Hendrik Lorentz, working at the end of the nineteenth century, gave the force law its modern form, describing the force on a charge moving through electric and magnetic fields. The law now carries his name, and it remains the standard description of the force, used in everything from textbook problems to the design of particle accelerators.

FAQ

What is the magnetic force in simple terms?

Magnetic force is the push or pull that a magnetic field exerts on a moving electric charge or on a wire carrying a current. A charge that is not moving feels no magnetic force. The force always acts at a right angle to both the motion of the charge and the direction of the field, so it steers a moving charge rather than speeding it up or slowing it down.

What is the formula for magnetic force?

For a single charge, the magnetic force is F = qvB sin(theta), where q is the charge in coulombs, v is its speed in meters per second, B is the magnetic field strength in tesla, and theta is the angle between the velocity and the field. For a straight wire carrying a current, the force is F = ILB sin(theta), where I is the current in amps and L is the length of the wire in meters. The full Lorentz force law, which includes an electric field as well, is F = q(E + v x B).

Does magnetic force act on a stationary charge?

No. A stationary charge feels no magnetic force, no matter how strong the field is. The force depends on the velocity of the charge, so when the velocity is zero, the force is zero. A stationary charge can still feel an electric force, but magnetic force requires motion.

Why does magnetic force do no work?

Work is done when a force acts along the direction of motion, adding or removing energy. The magnetic force always acts at a right angle to the motion, so it has no component along the direction of travel. It can change the direction of a charged particle, bending its path into a circle or a spiral, but it cannot change its speed, so its kinetic energy stays the same.

What is the difference between magnetic force and the force between magnets?

Magnetic force on a charge acts only on a moving charge, and it pushes sideways to the motion. The force between two magnets acts on magnetic dipoles, which are objects with a north and a south pole, and it acts even when nothing is moving. The two effects are related, because the magnetism of a bar magnet comes from the motion and alignment of charges inside it, but they follow different rules and should not be confused.

How does a magnet attract iron?

A magnet creates a magnetic field around itself. When a piece of iron is placed in that field, the tiny magnetic dipoles inside the iron line up with the field, turning the iron into a temporary magnet. The field of the original magnet then pulls on that temporary magnet. The effect is strongest for ferromagnetic materials, principally iron, nickel, and cobalt.

What is the unit of magnetic force?

Magnetic force is measured in newtons, symbol N, the same unit as every other force. The strength of the magnetic field that produces the force is measured in tesla, symbol T, and in the older unit the gauss, symbol G, where 1 tesla equals 10,000 gauss. The field of the Earth at the surface is about 0.25 gauss to 0.65 gauss, or about 25 to 65 microtesla.

How is magnetic force used in an electric motor?

In a motor, coils of wire carrying current sit inside a magnetic field. The field exerts a force on each side of a coil, and because the current flows in opposite directions on the two sides, the forces point in opposite directions and turn the coil. A commutator reverses the current at the right moment on each half turn, so the coil keeps turning in the same direction. The turning of the coil is the mechanical output of the motor.

Can magnetic force levitate a train?

Yes, in the sense that magnetic forces can support a train without wheels touching a rail. In a maglev train, magnets on the train and magnets or coils in the track repel or attract each other with enough force to lift the train a short distance above the track, and other magnets propel it forward. The lift is a magnetic force between magnets and currents, not the force on a single moving charge, but it follows from the same principle that magnetic fields exert forces on magnets and currents.

Is magnetic force the same as gravity?

No. Gravity acts on mass and always attracts, while magnetic force acts on moving charge and can attract or repel depending on direction and on the sign of the charge. Gravity is also far weaker than the electromagnetic force. The two are separate fundamental forces, although both can be described with field language, and both act at a distance without contact.

Sources & references

• Encyclopaedia Britannica, "Magnetic force", https://www.britannica.com/science/magnetic-force (definition of magnetic force as attraction or repulsion between electrically charged particles because of their motion; force proportional to charge, velocity, field, and sine of the angle; electric motors and attraction of magnets for iron as basic effects). Page updated 26 September 2026.
• HyperPhysics, Georgia State University, "Magnetic forces", https://hyperphysics.phy-astr.gsu.edu/hbase/magnetic/magfor.html (magnetic field defined from the Lorentz Force Law; force perpendicular to velocity and field; F = qvB sin(theta); zero force on a stationary charge or a charge moving parallel to the field; right-hand rule; tesla equals 10,000 gauss; Earth's field on the order of half a gauss).
• Georgia Institute of Technology, Physics Book, "Introduction to Magnetic Force", https://www.physicsbook.gatech.edu/Introduction_to_Magnetic_Force (force acts on moving charges and currents; perpendicular to velocity and field; electromagnetic force second strongest of the four fundamental forces; F = qvB sin(theta) and F = ILB sin(theta); worked examples 5.196 newtons and 0.36 newtons; MRI connection; neutron stars and magnetars; Oersted 1820 and Maxwell's Treatise).
• University of California, Santa Barbara, ScienceLine, "Earth's magnetic field", http://scienceline.ucsb.edu/getkey.php?key=6637 (Earth's field generated by flowing currents of molten iron in the outer core; surface field 0.25 gauss to 0.65 gauss; motor and generator are the same machine run in opposite directions; a motor driving a generator always delivers less energy than it takes in).