First slide

Magnetic dipole in a uniform magnetic field

Question

A bar magnet suspended freely in uniform magnetic field is vibrating with a time period of 3 seconds. If the field strength is increased to four times of the earlier field strength, the time period will be (in seconds)

Moderate

Solution

$\begin{array}{rcl} 3 & = & 2 π \sqrt{\frac{I}{MB}} \to (1) \\ T & = & 2 π \sqrt{\frac{I}{4 MB}} \to (2) \\ \frac{(1)}{(2)}, \frac{3}{T} & = & \sqrt{\frac{4}{1}} = 2, \\ T & = & \frac{3}{2} = 1.5 \sec \end{array}$

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