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