Magnetism Question 227
Question: A coil in the shape of an equilateral triangle of side l is suspended between the pole pieces of a permanent magnet such that $ \vec{B} $ is in plane of the coil. If due to a current i in the triangle a torque $ \tau $ acts on it, the side l of the triangle is
Options:
A) $ \frac{2}{\sqrt{3}}{{( \frac{\tau }{B.i} )}^{\frac{1}{2}}} $
B) $ 2{{( \frac{\tau }{\sqrt{3}B.i} )}^{\frac{1}{2}}} $
C) $ \frac{2}{\sqrt{3}}( \frac{\tau }{B.i} ) $
D) $ \frac{1}{\sqrt{3}}\frac{\tau }{B.i} $
Show Answer
Answer:
Correct Answer: B
Solution:
[b] $ \tau =MB,\sin ,\theta ,,\tau =iAB,\sin ,90^{o} $
$ \
Therefore ,,,,A=\frac{\tau }{iB}=1/2(BC)(AD) $ But $ \frac{1}{2},(BC)(AD) $
$ =\frac{1}{2}(l)\sqrt{l^{2}-{{( \frac{l}{2} )}^{2}}}=\frac{\sqrt{3}}{4}l^{2} $
$ \Rightarrow ,,,\frac{\sqrt{3}}{4}{{(l)}^{2}}=\frac{\tau }{Bi}\Rightarrow ,\
Therefore ,,,l=2{{( \frac{\tau }{\sqrt{3}B.i} )}^{\frac{1}{2}}} $
BETA
