First slide

Magnetic dipole in a uniform magnetic field

Question

The strength of the magnetic field in which the magnet of a vibration magnetometer is oscillating is increased 4 times its original value. The frequency of oscillation would then become

Easy

A

Twice its original value
B

four times its original value
C

half its original value
D

one-fourth its original value

Solution

(1)
$\begin{array}{l} T = 2 π \sqrt{\frac{I}{B M}} \\ ∴ f = \frac{1}{T} \propto \sqrt{B} \\ ∴ \frac{f^{'}}{f} = \sqrt{\frac{B^{'}}{b}} = \sqrt{\frac{4 B}{B}} = 2 \end{array}$

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