Why Magnetic Force Does No Work on a Charge

Physics · Moving Charges And Magnetism · NEET

A magnetic force does no work on a charge because the force F = qv x B is always perpendicular to the velocity v. Work needs a force component along the motion, but here that component is zero, so kinetic energy and speed never change. Memory hook: "Magnetic force only turns you, it never speeds you up or slows you down."
Magnetic force is always perpendicular to velocity (F . v = 0)+qvF = qv x BForce bends path, speed stays constantB (out of page)v turns, |v| never changes
The magnetic force F = qv x B (red) is always at 90 degrees to velocity v (green), so it bends the path into a circle while keeping speed and kinetic energy constant.

Your doubts, answered

If the magnetic force does no work, how can it make the charge move in a circle?

Doing work and applying a force are different things. The magnetic force is a real force, so it can change the direction of velocity, which is what circular motion needs. Work is only done when a force has a component along the direction of motion. Since F = qv x B stays perpendicular to v, it bends the path without ever adding or removing kinetic energy. So it curves you, but your speed stays the same.

Does the magnetic force change the velocity or not?

It changes velocity but not speed. Velocity is a vector (size + direction). The magnetic force changes only the direction of v, never its magnitude. So |v| (speed) is constant, but the direction keeps turning. That is why the charge moves in a circle or helix at constant speed.

Why is F = qv x B always perpendicular to velocity?

By the rule of the cross product, v x B is always perpendicular to both v and B. So the magnetic force F = qv x B is perpendicular to v no matter what angle v makes with B. Because the force is always at 90 degrees to the motion, the power delivered P = F.v = 0 at every instant.

So can the magnetic force ever change kinetic energy?

No. Work-energy theorem says change in kinetic energy = work done. The magnetic force does zero work, so kinetic energy is unchanged, which means speed is unchanged. If you ever see a problem where a charge speeds up or slows down, an electric field (or some other force) must be doing that work, not the magnetic field.

What if the charge moves parallel to B?

Then the angle between v and B is 0 degrees, so v x B = 0 and the magnetic force is zero. The charge moves in a straight line with no deflection. This case appears often in NEET: a charge fired along B feels no magnetic force at all.

⚠️ The NEET trap
A magnetic field can speed up a charged particle, so it changes the particle's kinetic energy.
A magnetic force is always perpendicular to velocity, so it does zero work and cannot change speed or kinetic energy. Only an electric field can change a charge's speed.
🧠 If the question shows a charge speeding up or slowing down, look for an electric field. The magnetic part never does the work.

Real NEET questions

NEET 2023 Phase 2

A uniform electric field and a uniform magnetic field are acting along the same direction in a certain region. If an electron is projected in the region such that its velocity is pointed along the direction of the fields, then the electron

A · Speed will decrease
B · Speed will increase
C · Will turn towards right of direction of motion
D · Will turn towards left of direction of motion
Solution: Step 1: Velocity v is parallel to B. So the magnetic force F = q(v x B) = qvB sin(0) = 0. The magnetic field does nothing here (no deflection, no work). Step 2: Only the electric force acts. For an electron (charge = -e), F = -eE, which points opposite to E. Step 3: Since v points along E, this electric force is opposite to v, so the electron decelerates. Its speed decreases. Note: the magnetic force could never change the speed anyway (it does no work) - the speed change is entirely due to the electric field. Answer: A.

Solved Moving Charges And Magnetism NEET PYQs

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Frequently asked

Why does the magnetic force do no work on a charge?

Because F = qv x B is always perpendicular to the velocity v. Power delivered is P = F.v = 0 at every instant, so no work is done and kinetic energy stays constant.

Does a magnetic force change the speed of a charged particle?

No. It only changes the direction of velocity. Speed and kinetic energy remain constant because the force is always at 90 degrees to the motion.

Then how does a charge move in a circle in a magnetic field?

The perpendicular magnetic force acts as the centripetal force. It continuously turns the velocity without changing its magnitude, giving circular motion at constant speed.

Can any field change a charge's kinetic energy?

Yes, an electric field can, because the electric force qE can have a component along the velocity. The magnetic force alone never does.

What happens if the velocity is parallel to the magnetic field?

The angle is 0 degrees, so v x B = 0 and the magnetic force is zero. The charge moves straight with no deflection.