First slide

The bar magnet

Question

Two bar magnets of different lengths produce magnetic field induction of same magnitude at points on the axial line, at the same distance in each case. Then

Moderate

A

Magnetic moment is same for both magnets
B

Magnetic moment is more for short magnet
C

Magnetic moment is more for longer magnet
D

We cannot decide which has more magnet moment

Solution

Magnetic field on the axial line of a bar magnet is given by
$B = \frac{μ_{0}}{4 π} \frac{2 M d}{{(d^{2} - l^{2})}^{2}} i f t w o m a g n e t s p r o d u c e s a m e m a g n e t i c f i e l d \frac{M_{1}}{M_{2}} = \frac{{(d^{2} - {l_{1}}^{2})}^{2}}{{(d^{2} - l_{2}^{2})}^{2}} i f l_{1} > l_{2} t h e n M_{1} < M_{2}$

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