Magnetic Force in AP Physics C: Electricity and Magnetism

In AP Physics C: E&M, magnetic force is the force a magnetic field exerts on a moving charge (F = qv × B) or a current-carrying wire (F = IL × B). It always points perpendicular to both the motion and the field, so it can change a charge's direction but never its speed.

What is Magnetic Force?

Magnetic force is what a magnetic field does to moving charge. A charge sitting still in a magnetic field feels nothing. Once it moves, it feels a force given by the cross product F = qv × B, with magnitude qvB sinθ. The cross product is the whole story. The force is perpendicular to both v and B, and you find its direction with the right-hand rule (then flip it for a negative charge).

A current is just a lot of moving charge, so a wire in a field feels a force too. For a straight wire in a uniform field that's F = IL × B. For a curved wire or a nonuniform field you add up the pieces with F_B = ∫I(dℓ × B). Because the force is always perpendicular to velocity, it does zero work on a point charge. Think of it as a steering force. It bends paths into circles and spirals but can't speed anything up or slow it down.

Why Magnetic Force matters in AP® Physics C: E&M

Magnetic force is the core idea of Unit 12 (Magnetic Fields and Electromagnetism). It shows up in topic 12.1 (Magnetic Fields), where you meet F = qv × B for charges, and in topic 12.3 (Magnetic Fields of Current-Carrying Wires and the Biot-Savart Law), where one wire's field pushes on another wire. It carries straight into Unit 13 (Electromagnetic Induction) through topic 13.3 (Induced Currents and Magnetic Forces). There, the force on an induced current is what makes a moving rod slow down. If you can set up the cross product, find directions, and connect force to motion, you can handle a large share of the E&M magnetism questions.

How Magnetic Force connects across the course

Lorentz Force Law (Unit 12)

Magnetic force is half of the Lorentz force. The full law is F = q(E + v × B). The electric part pushes along the field, and the magnetic part steers sideways. Velocity-selector style problems are just these two halves set equal and opposite.

Centripetal Motion (Unit 12)

Since magnetic force is always perpendicular to velocity, it acts like a string holding a ball in a circle. Set qvB = mv²/r and you get the radius r = mv/(qB). This is the mechanics you already know, with the magnetic force cast as the centripetal force.

Biot-Savart Law and Parallel Wires (Unit 12)

One wire makes a field (Biot-Savart or Ampère), and a second wire feels a force in that field (F = IL × B). Put those together and you get F/L = μ₀I₁I₂/(2πd). Same-direction currents attract and opposite-direction currents repel.

Induced Currents and Magnetic Braking (Unit 13)

When a rod slides on rails through a field, motion induces a current. That current then feels a magnetic force that opposes the motion, which is Lenz's law showing up as a force. This is why a sliding rod slows down and why mechanical energy ends up as heat in the resistor.

Is Magnetic Force on the AP® Physics C: E&M exam?

Expect magnetic force in both MCQ and FRQ, often mixed with mechanics.

• Direction questions. You'll be asked which way a charge deflects or which way a wire gets pushed. Use the right-hand rule and watch the sign of the charge.
• Wire-on-wire forces. Practice problems ask for force per unit length between parallel wires. For example, 8.0 A and 12.0 A wires 5.0 cm apart give F/L = μ₀I₁I₂/(2πd) ≈ 3.8 × 10⁻⁴ N/m, attractive since the currents are parallel. Others ask what current makes the magnetic force on a wire balance its weight, which comes from setting F/L equal to (mass per length)·g.
• Maximizing force. A classic MCQ twist asks for the maximum force on a flexible wire. The answer is ILB, reached when the wire is straight and perpendicular to B (for L = 0.5 m, I = 8.0 A, B = 0.4 T, that's 1.6 N).
• Superposition. Multiple wires (parallel or perpendicular) mean you add field or force vectors from each one.
• Released FRQs. 2025 FRQ Q4 used long parallel wires carrying equal, opposite currents, where you have to reason about the field and force they produce. 2023 FRQ Q2 put a rod on conducting rails with a resistor and a spring, so the magnetic force on the induced current had to be combined with spring force and Newton's second law.

What you need to DO is set up the cross product, get the direction right, and plug the magnetic force into F = ma, a circular-motion equation, or an energy argument.

Magnetic Force vs Electric Force

Electric force (F = qE) acts on any charge, moving or not, and points along the field line, so it can do work and change speed. Magnetic force (F = qv × B) acts only on moving charge and points perpendicular to the field and the velocity, so it does no work on a point charge. A quick check is to ask whether the charge would still feel the force at rest. If yes, it's electric.

Key things to remember about Magnetic Force

• Magnetic force on a point charge is F = qv × B, so a charge at rest or moving parallel to B feels no magnetic force at all.

• The force on a current-carrying wire is F = IL × B for a straight wire in a uniform field, and F = ∫I(dℓ × B) in general.

• Magnetic force is always perpendicular to velocity, so it does zero work on a point charge and only changes direction, not speed.

• A charge moving perpendicular to a uniform field travels in a circle of radius r = mv/(qB), because magnetic force supplies the centripetal force.

• Parallel wires with currents in the same direction attract, and wires with currents in opposite directions repel, with F/L = μ₀I₁I₂/(2πd).

• In induction problems, the magnetic force on the induced current always opposes the motion that caused it, which is why sliding rods decelerate.

Frequently asked questions about Magnetic Force

What is magnetic force in AP Physics C E&M?

It's the force a magnetic field exerts on a moving charge, F = qv × B, or on a current, F = IL × B. Its direction is perpendicular to both the velocity (or current) and the field, and you find it with the right-hand rule.

Does magnetic force do work on a charged particle?

No. Because the force is always perpendicular to velocity, it does zero work on a point charge, and the particle's speed and kinetic energy stay constant. It only bends the path, which is why charges in uniform fields move in circles.

How is magnetic force different from electric force?

Electric force (qE) acts on any charge and points along the field, so it can speed charges up. Magnetic force (qv × B) only acts on moving charges and points sideways to both v and B. Combined, they make the Lorentz force F = q(E + v × B).

Do parallel wires with current attract or repel?

It depends on direction. Currents in the same direction attract and currents in opposite directions repel. 2025 FRQ Q4 used two parallel wires carrying equal currents in opposite directions, so knowing this rule matters on the real exam.

Why does a rod sliding on rails in a magnetic field slow down?

The rod's motion induces a current, and the field exerts a magnetic force IL × B on that current that points opposite the motion (Lenz's law). 2023 FRQ Q2 built a full problem around this, combining the magnetic force with a spring and a resistor.