First slide

Magnetism

Question

The ratio of magnetic moments of two short magnets which give null deflection in Tan B position at 24 cm and 18 cm from the centre of a deflection magnetometer is

Moderate

A

2 : 3
B

64 : 27
C

27 : 64
D

4: 9

Solution

At the Tan B position , the strength of the magnetic moment at the magnetometer is proportional to the cube of the distance between the magnetometer and center of deflection of the magnetometer.
$∴ \frac{M_{1}}{d_{1}^{3}} = \frac{M_{2}}{d_{2}^{3}} \Rightarrow \frac{M_{1}}{M_{2}} = {(\frac{d_{1}}{d_{2}})}^{3} \Rightarrow \frac{M_{1}}{M_{2}} = {(\frac{24}{18})}^{3} \Rightarrow M_{1} : M_{2} = 64 : 27$

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