Question

A conductor (shown in the figure) carrying constant current $I$ is kept in the $x-y$ plane in a uniform magnetic field $\vec{B}$. If $F$ is the magnitude of the total magnetic force acting on the conductor, then the correct statement(s) is(are)

• A. If $\vec{B}$ is along $\hat{z}$ , F $\propto$$ (L + R)$
• B. If $\vec{B}$ is along $\hat{x}$ , $F = 0$
• C. If $\vec{B}$ is along $\hat{y}$ , F $\propto$ (L + R)
• D. If $\vec{B}$ is along $\hat{z}$ , $F = 0$

Answer 1

Answer: (A), (B), (C)

Option A if B is along z axis i.e B$\hat{k}$
$\overrightarrow{i\ell} = 2i\left(L+R\right) \hat{i}$
$\vec{F} = \overrightarrow{i\ell}\times\vec{B}\quad\quad⇒ F = 2i \left(L + R\right) \hat{i} × \vec{B}\,\hat{k}$
$∴ F ∝ \left(L + R\right)\quad\quad$ option A is correct answer.
Option B if B is along x axis i.e B$\hat{i}$
then $F = 2i \left(L + R\right) \hat{i} × \left(B\hat{i} \right) = 0\quad\quad$ option B is correct answer
Option C if B is along y axis i.e. B$ \hat{j}$
then $F = 2i \left(L + R\right) \hat{i} × B \hat{j}$
$| F | ⇒ 2i \left(L + R\right) B$
$∴ F ∝ \left(L + R\right)\quad\quad$ option $\left(C\right)$ is correct answer.