First slide

Magnetic dipole in a uniform magnetic field

Question

The period of oscillations of a magnetic needle in a magnetic field is 1.0 s If the length of the needle is halved by cutting it then the time period will be

Easy

A

1.0 s
B

0.5 s
C

0.25 s
D

2.0 s

Solution

We know that
$T = 2 π \sqrt{(\frac{I}{{MB}_{H}})}$
When length is halved, M is also halved and I becomes (1/8)
$∴ T^{'} = 2 π \sqrt{(\frac{I \times 2}{8 \times {MB}_{H}})} = \frac{1}{2} T = \frac{1 \cdot 0}{2} = 0 \cdot 5 second$

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