A rectangular loop of wire, supporting a mass m, hangs with one end in a uniform magnetic field B pointing into the plane of the paper. A clockwise current is set up such that i > mg/Ba, where a is the width of the loop. Then: (a) The weight rises due to a vertical force caused by the magnetic field and work is done on the system. (b) The weight does not rise due to a vertical force caused by the magnetic field and work is done on the system. (c) The weight rises due to a vertical force caused by the magnetic field but no work is done on the system. (d) The weight rises due to a vertical force caused by the magnetic field and work is extracted from the magnetic field.

Answer: (a). Clockwise current: in the top side PQ the current flows along +x; B is into the page ( -k). F = i a i×(-Bk) = iaB j: upward. Forces on the vertical sides cancel. iaB > mg, so the weight rises. The magnetic force itself does no work; the energy comes from the source driving the current, i.e. work is done on the system. So the answer is (a).

A rectangular loop of wire, supporting a mass m, hangs with one end… | JEE Main 2013 (23 Apr, Shift 1)

Q59JEE Main 2013 · 23 APR · SHIFT 1Medium

Force on Current-Carrying Conductors

A rectangular loop of wire, supporting a mass m, hangs with one end in a uniform magnetic field $\vec{B}$ pointing into the plane of the paper. A clockwise current is set up such that $i > mg/Ba$ , where a is the width of the loop. Then:

Show answer and solution

Answer: (a)

Clockwise current: in the top side PQ the current flows along $+x$ ; $\vec{B}$ is into the page ( $-\hat{k}$ ).
$\vec{F} = i a\,\hat{i}\times(-B\hat{k}) = iaB\,\hat{j}$ : upward. Forces on the vertical sides cancel.
$iaB > mg$ , so the weight rises.
The magnetic force itself does no work; the energy comes from the source driving the current, i.e. work is done on the system.
So the answer is (a).

Report a mistake

Force on Current-Carrying Conductors question from JEE Main 2013 (23 Apr, Shift 1)

More questions on Force on Current-Carrying Conductors