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Two short magnets AB and CD are in the X – Y plane and are parallel to x-axis and the coordinates of their centers respectively are (0, 2) and (2, 0). Line joining the North - South poles of CD is opposite to that of AB and lies along the positive X-axis. The resultant field induction due to AB and CD at a point P(2, 2) is 100×10^–7T. When the poles of the magnet CD are reversed the resultant field induction is 50×10^–7T. The values of magnetic moments of AB and CD (in Am²) are

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300, 200

600, 400

300, 150

200, 100

answer is A.

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Detailed Solution

$\vec{B_{AB}} + \vec{B_{CD}} = 100 \times 10^{- 7}$

$\vec{B_{AB}} - \vec{B_{CD}} = 50 \times 10^{- 7}$

$\Rightarrow \vec{B_{AB}} = 75 \times 10^{- 7} and {\vec{B}}_{CD} = 25 \times 10^{- 7}$

For AB, point P lies on axial line,

$B_{AB} = \frac{μ_{o} 2 M_{AB}}{4 π {(2)}^{3}}$

$\Rightarrow M_{AB} = 300$

For CD, point P lies on equatorial line,

$B_{CD} = \frac{μ_{o} M_{AB}}{4 π {(2)}^{3}}$

$\Rightarrow M_{CD} = 200$

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