Question

Derive an expression for magnetic force `vecF` acting on a straight conductor of length L carrying current I in an external magnetic field `vecB`. Is it valid when the conductor is in zig-zag form? Justify.

Answer 1

Since the force on an individual charge moving at the drift velocity v_d,

F = qv_d B sin θ

For N charge carriers

F = (qv_d B sin θ)(N)

where, N = nV = nAL

⇒ F = qv_d B sin θ nAL

F = nq Av_d B sin θL

F = ILB sin θ    ...[ ∴ I = nq Av_d]

`vecF = I(vecL xx vecB)`

Yes, that is true even when the conductor is zigzag-shaped since the wire's length will still be at the same angle to the magnetic field.