Magnetism Question 247
Question: Two identical short bar magnets, each having magnetic moment of $ 10,Am^{2} $ , are arranged such that their axial lines are perpendicular to each other and their centres be along the same straight line in a horizontal plane. If the distance between their centres is 0.2 m, the resultant magnetic induction at a point midway between them is $ ({\mu _{0}}=4\pi \times {{10}^{-7}},H{{m}^{-1}}) $
Options:
A) $ \sqrt{2}\times {{10}^{-7}},tesla $
B) $ \sqrt{5}\times {{10}^{-7}},tesla $
C) $ \sqrt{2}\times {{10}^{-3}},tesla $
D) $ \sqrt{5}\times {{10}^{-3}},tesla $
Show Answer
Answer:
Correct Answer: D
Solution:
[d] From figure $ B _{net}=\sqrt{B _{a}^{2}+B _{e}^{2}} $
$ =\sqrt{{{( \frac{{\mu _{0}}}{4\pi }.\frac{2M}{d^{3}} )}^{2}}+{{( \frac{{\mu _{0}}}{4\pi }.\frac{M}{d^{3}} )}^{2}}} $
$ =\sqrt{5}.\frac{{\mu _{0}}}{4\pi }.\frac{M}{d^{3}}=\sqrt{5}\times {{10}^{-7}}\times \frac{10}{{{(0.1)}^{3}}}=\sqrt{5}\times {{10}^{-3}},tesla $
BETA
