The magnetic field strength at a point at a distance d from the centre on the axial line of a very short bar magnet of Magnetic moment $M$ is $B$ . The Magnetic induction at a distance $2 d$ from the centre on the equatorial line of a Magnetic Moment $8 M$ will be

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Answer 1

$B = \frac{2 μ _{0} m}{4 π d ^{3}}$

$B e q u a t o r i a l = \frac{μ _{0} m}{4 π d ^{3}}$

$d_{1} = d$
$d_{2} = 2 d$
Also,
$m_{1} = M$
$m_{2} = 8 M$

$B_{1} = \frac{2 μ _{0} m}{4 π d ^{3}} . . . . . . . . . . . . 1$

$B_{2} = \frac{2 μ _{0} m}{4 π d ^{3}} = \frac{μ _{0} 8 M}{4 π ( 2 d ) ^{3}} . . . . . . . . . 2$
From 1 & 2 we get that,
$B_{e q u a t o r i a l} = \frac{B}{2}$

Answer 2

B = \frac{2 μ _{0} m}{4 π d ^{3}}

B e q u a t o r i a l = \frac{μ _{0} m}{4 π d ^{3}}

d_{1} = d

d_{2} = 2 d

Also,

m_{1} = M

m_{2} = 8 M

B_{1} = \frac{2 μ _{0} m}{4 π d ^{3}} . . . . . . . . . . . . 1

B_{2} = \frac{2 μ _{0} m}{4 π d ^{3}} = \frac{μ _{0} 8 M}{4 π ( 2 d ) ^{3}} . . . . . . . . . 2

From 1 & 2 we get that,

B_{e q u a t o r i a l} = \frac{B}{2}