A charge Q is moving dl⃗ distance in the magnetic field B⃗. Find the value of work done by B⃗.

Solution

Physics sir · 3 steps

The magnetic force always pushes sideways to the motion, so it can never do any work on the charge.

1. Direction of force. The magnetic force on a moving charge is F⃗ = Q(v⃗ × B⃗). A cross product is perpendicular to both vectors, so F⃗ is always perpendicular to v⃗.
2. Direction of displacement. In a small time dt the charge moves dl⃗ = v⃗ dt. So dl⃗ points along v⃗, and the force is perpendicular to dl⃗ as well.

   dW = F⃗ · dl⃗ = Q(v⃗ × B⃗) · v⃗ dt = 0

3. So. The dot product of two perpendicular vectors is zero, so the work done by B⃗ is zero on every bit of the path, whatever its shape. The answer is (a).

The idea to keep. A magnetic field can turn a charge but cannot speed it up or slow it down. Its force is always perpendicular to the velocity, so it does zero work and the kinetic energy stays the same.

Answer from the NTA final answer key. Solution by PrepWiser.