Torque is the rotational equivalent of force, defined as τ = r × F, measuring how effectively a force twists an object about an axis. In AP Physics C: E&M, torque appears when a magnetic field exerts forces on a current-carrying loop, producing the rotation that drives electric motors.
Torque is what force becomes when you care about rotation instead of straight-line motion. Mathematically, τ = r × F, a cross product between the position vector (from the axis to where the force acts) and the force itself. Its magnitude is rF sinθ, so only the part of the force perpendicular to the lever arm actually twists anything. Push on a door at its hinges and nothing happens; push at the handle and it swings. Same force, different torque.
In AP Physics C: Electricity & Magnetism, torque earns its spot in Unit 4 because magnetic fields exert forces on current-carrying wires (F = IL × B). Put a closed loop of current in a uniform field and the net force on it is zero, but the forces on opposite sides point in opposite directions at different positions, so the net torque is not zero. The loop twists until its magnetic moment lines up with the field. That torque is τ = NIAB sinθ for a loop with N turns, current I, and area A, and it is literally how every electric motor works.
Torque lives in Topic 4.2, Current-Carrying Wires & Magnetic Fields, where you analyze the forces and torques a magnetic field exerts on currents. It's also the conceptual bridge between Mechanics and E&M. You learned τ = r × F and τ = Iα (rotational Newton's second law) in Physics C: Mechanics, and E&M asks you to apply that same machinery to a current loop in a field. If you can find the force on each segment of a loop with the right-hand rule and then sum the torques about the rotation axis, you can derive τ = NIAB sinθ from scratch, which is exactly the kind of derivation Physics C rewards. Torque on a loop is also the physical principle behind galvanometers and DC motors, the standard real-world hooks for this topic.
Keep studying AP Physics C: E&M Unit 4
Right-Hand Rule (Unit 4)
You can't find the torque on a current loop without first finding the direction of F = IL × B on each side of the loop. The right-hand rule gives you those force directions, and the torque is just those forces acting at a distance from the rotation axis.
Moment Arm / Lever Arm (Mechanics)
The lever arm is the perpendicular distance from the axis to the line of the force, and torque equals force times lever arm. For a rectangular current loop, the lever arm is set by the loop's geometry, which is why the loop's area A shows up in τ = NIAB sinθ.
Angular Acceleration (Mechanics)
Net torque causes angular acceleration through τ = Iα, the rotational version of F = ma. A magnetic torque on a current loop doesn't just exist on paper; it spins the loop, which is the whole point of a motor.
EMF and Electromagnetic Induction (Unit 5)
Run the motor story backwards and you get a generator. An external torque spins a loop in a magnetic field, the changing flux induces an EMF, and the induced current creates a counter-torque opposing the spin (Lenz's law). Torque is the mechanical half of the energy conversion in both devices.
Expect torque in multiple-choice stems like "a rectangular loop carrying current I sits in a uniform magnetic field B; what is the magnitude of the torque?" or ranking tasks comparing loop orientations (torque is max when the loop's plane is parallel to B, zero when the magnetic moment is aligned with B). On free-response, the classic move is a derivation. You're given a loop in a field and asked to find the force on each side using F = IL × B, then sum torques about an axis to get τ = NIAB sinθ. No released FRQ is needed to predict this; it's the standard analysis Topic 4.2 builds toward. Watch the two big traps. First, the net force on a closed loop in a uniform field is zero even when the net torque isn't. Second, the angle θ in τ = NIAB sinθ is between the field and the loop's normal (magnetic moment), not the plane of the loop.
Torque and work both have units of newton-meters, but they are completely different quantities. Work is a scalar from a dot product (F · d) and transfers energy. Torque is a vector from a cross product (r × F) and causes angular acceleration. By convention you write torque in N·m and never in joules, precisely because torque is not energy.
Torque is the rotational equivalent of force, defined by the cross product τ = r × F with magnitude rF sinθ.
A current loop in a uniform magnetic field feels zero net force but a nonzero net torque of τ = NIAB sinθ, where θ is measured between the field and the loop's normal.
Torque is maximum when the plane of the loop is parallel to the magnetic field and zero when the loop's magnetic moment is aligned with the field.
Use the right-hand rule on F = IL × B for each segment of the loop to figure out which way the loop rotates.
This torque is the operating principle of DC motors and galvanometers, and it connects directly back to τ = Iα from Mechanics.
Torque and work share the unit N·m, but torque is a vector that causes rotation while work is a scalar that transfers energy.
Torque is the rotational effect of a force, τ = r × F. In E&M it specifically describes the twist a magnetic field puts on a current-carrying loop, given by τ = NIAB sinθ, which is the physics behind electric motors.
Yes, in a uniform field the net force on a closed loop is zero because the forces on opposite sides cancel. But those forces act at different positions, so the net torque is generally not zero, and the loop rotates.
It's the angle between the magnetic field and the normal to the loop (the direction of the magnetic moment), not the plane of the loop itself. So torque is maximum when the loop's plane is parallel to B and zero when the normal lines up with B. Mixing this up is one of the most common point-losers.
Force changes linear motion (F = ma); torque changes rotational motion (τ = Iα). Torque depends on where the force is applied, since τ = rF sinθ. The same force applied far from the axis produces a bigger torque than one applied close to it.
Both come out to newton-meters, but work is a dot product (a scalar, an energy transfer) while torque is a cross product (a vector that causes rotation). By convention torque stays in N·m and is never written in joules.