Magnetism Question 134
Question: A magnet oscillating in a horizontal plane has a time period of 2 second at a place where the angle of dip is 30o and 3 seconds at another place where the angle of dip is 60o. The ratio of resultant magnetic fields at the two places is
[Pb. PET 2001]
Options:
A) $ \frac{4\sqrt{3}}{7} $
B) $ \frac{4}{9\sqrt{3}} $
C) $ \frac{9}{4\sqrt{3}} $
D) $ \frac{9}{\sqrt{3}} $
Show Answer
Answer:
Correct Answer: C
Solution:
$ T\propto \frac{1}{\sqrt{B _{H}}}=\frac{1}{\sqrt{B\cos \varphi }} $
$ \Rightarrow \frac{T _{1}}{T _{2}}=\sqrt{\frac{B _{2}\cos {\varphi _{2}}}{B _{2}\cos {\varphi _{1}}}} $
$ \Rightarrow \frac{B _{1}}{B _{2}}=\frac{T _{2}^{2}}{T _{1}^{2}}\times \frac{\cos {\varphi _{2}}}{\cos {\varphi _{1}}}={{( \frac{3}{2} )}^{2}}\times \frac{\cos 60}{\cos 30} $
$ \Rightarrow \frac{B _{1}}{B _{2}}=\frac{9}{4\sqrt{3}} $
BETA
