Magnetism Question 37
Question: Two short magnets of equal dipole moments M are fastened perpendicularly at their centre (figure). The magnitude of the magnetic field at a distance d from the centre on the bisector of the right angle is
Options:
A) $ \frac{{\mu _{0}}}{4\pi }\frac{M}{d^{3}} $
B) $ \frac{{\mu _{0}}}{4\pi }\frac{M\sqrt{2}}{d^{3}} $
C) $ \frac{{\mu _{0}}}{4\pi }\frac{2\sqrt{2}M}{d^{3}} $
D) $ \frac{{\mu _{0}}}{4\pi }\frac{2M}{d^{3}} $
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Answer:
Correct Answer: C
Solution:
Resultant magnetic moment of the two magnets is $ M _{net}=\sqrt{M^{2}+M^{2}}=\sqrt{2}M $ Imagine a short magnet lying along OP with magnetic moment equal to $ M\sqrt{2} $ . Thus point P lies on the axial line of the magnet.
$ \
Therefore $ Magnitude of magnetic field at P is given by $ B=\frac{{\mu _{0}}}{4\pi }.\frac{2\sqrt{2}M}{d^{3}} $
BETA
