Magnetics 1 Question 17
17. A conductor (shown in the figure) carrying constant current $I$ is kept in the $x-y$ plane in a uniform magnetic field $\mathbf{B}$. If $F$ is the magnitude of the total magnetic force acting on the conductor, then the correct statements is/are
(2015 Adv.)
(a) if $\mathbf{B}$ is along $\hat{\mathbf{z}}, F \propto(L+R)$
(b) if $\mathbf{B}$ is along $\hat{\mathbf{x}}, F=0$
(c) if $\mathbf{B}$ is along $\hat{\mathbf{y}}, F \propto(L+R)$
(d) if $\mathbf{B}$ is along $\hat{\mathbf{z}}, F=0$
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Answer:
Correct Answer: 17. (a,b.c)
Solution:
Force on the complete wire $=$ force on straight wire $P Q$ carrying a current $I$.
$$ \mathbf{F}=I(\mathbf{P Q} \times \mathbf{B})=I[{2(L+R) \hat{\mathbf{i}}} \times \mathbf{B}] $$
This force is zero if $\mathbf{B}$ is along $\hat{\mathbf{i}}$ direction or $x$-direction. If magnetic field is along $\hat{\mathbf{j}}$ direction or $\hat{\mathbf{k}}$ direction,
$$ |\mathbf{F}|=F=(I)(2)(L+R) B \sin 90^{\circ} $$
or $\quad F=2 I(L+R) B$ or $F \propto(L+R)$
