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Q.

A short current carrying solenoid has a magnetic dipole moment M. P is a point on its axial line at a distance d from the north-pole and at a distance 2d from the south-pole. The magnetic induction at P is

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a

$\frac{μ_{0}}{4 π} \frac{3 M}{d^{3}}$

b

$\frac{μ_{0}}{4 π} \frac{3 M}{4 d^{3}}$

c

$\frac{μ_{}}{4 π} \frac{2 M}{d^{3}}$

d

$\frac{μ_{0}}{4 π} \frac{3 M}{8 d^{3}}$

answer is B.

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Detailed Solution

$l e n g t h o f t h e d i p o l e i s d a n d d i s \tan c e o f t h e p o i n t f r o m t h e c e n t e r i s \frac{3 d}{2} f i e l d o n t h e a x i a l l i n e = \frac{μ_{0}}{4 π} \frac{2 M x}{{(x^{2} - l^{2})}^{2}} h e r e x = \frac{3 d}{2} a n d l = \frac{d}{2}$

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