Two short bar magnets each of magnetic moment of ${9 Am}^{2}$ are placed such that one is at x = - 3cm and the other at y =-3 cm. If their magnetic moments are directed along positive and negative X-direction respectively, then the resultant magnetic field at the origin is

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100 T

10 T

0.1 T

0. 001 T

answer is C.

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Detailed Solution

Magnetic field due to M₁ (axial point),

$B_{1} = \frac{μ_{0}}{4 π} \times \frac{2 M}{r^{3}} = 10^{- 7} \times \frac{2 \times 9}{27 \times 10^{- 6}} = \frac{2}{3} \times 10^{- 1} T$

Magnetic field due to $M_{2}$ (equatorial point), $B_{2} = \frac{μ_{0}}{4 π} \times \frac{M}{r^{3}} = 10^{- 7} \times \frac{9}{27 \times 10^{- 6}} = \frac{1}{3} \times 10^{- 1} T$

$B = (\frac{1}{3} + \frac{2}{3}) \times 10^{- 1} T$ $\Rightarrow B = 10^{- 1} T = 0.1 T$

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