Magnetism Question 25
Question: Two identical magnetic dipoles of magnetic moments 1.0 A-m2 each, placed at a separation of 2m with their axis perpendicular to each other. The resultant magnetic field at a point midway between the dipoles is
[Roorkee 1995]
Options:
A) $ 5\times {{10}^{-7}}T $
B) $ \sqrt{5}\times {{10}^{-7}}T $
C) $ {{10}^{-7}}T $
D) None of these
Show Answer
Answer:
Correct Answer: B
Solution:
With respect to 1st magnet, P lies in end side-on position
$ \
Therefore B _{1}=\frac{{\mu _{0}}}{4\pi }( \frac{2M}{d^{3}} ) $ (RHS) With respect to 2nd magnet. P lies in broad side on position.
$ \
Therefore \ B _{2}=\frac{{\mu _{0}}}{4\pi }( \frac{M}{d^{3}} ) $ (Upward) $ B _{1}={{10}^{-7}}\times \frac{2\times 1}{1}=2\times {{10}^{-7}}T,\ B _{2}=\frac{B _{1}}{2}={{10}^{-7}}T $ As B1 and B2 are mutually perpendicular, hence the resultant magnetic field $ B _{R}=\sqrt{B _{1}^{2}+B _{2}^{2}}=\sqrt{{{(2\times {{10}^{-7}})}^{2}}+{{({{10}^{-7}})}^{2}}} $
$ =\sqrt{5}\times {{10}^{-7}}T $
BETA
