Magnetic Effects Of Current Question 450
Question: A circular arc QTS is kept in an external magnetic field $ {{\overset{\to }{\mathop{B}},}_{0}} $ as shown in figure. The arc carries a cur- rent I. The magnetic field is directed normal and into the page. The force acting on the arc is
Options:
A) $ 2IB_{0}R\hat{k} $
B) $ IB_{0}R\hat{k} $
C) $ -2IB_{0}R\hat{k} $
D) $ -IB_{0}R\hat{k} $
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Answer:
Correct Answer: B
Solution:
[b] We know, $ \overset{\to }{\mathop{F}},=I(\overset{\to }{\mathop{\ell }},\times \overset{\to }{\mathop{B}},) $ or
$ d\overset{\to }{\mathop{F}},=IB,d\ell ,\sin ,\theta $
$ \therefore F=\int_{60^{o}}^{120^{o}}{IB_{0},d\ell },\sin ,\theta ,d\ell $ where, $ d\ell =rd\theta $
$ F=\int_{60^{o}}^{120^{o}}{IB_{0},R,\sin ,\theta ,d\theta =IBR[ -\cos \theta ]_{60^{o}}^{120^{o}}} $
$ =IB_{0}R[ -( -\frac{1}{2} )+( \frac{1}{2} ) ]=IB_{0}R $ Hence, force acting on the arc is $ IB_{0}R\hat{k} $ .
BETA
