First slide

Magnetic dipole in a uniform magnetic field

Question

A long bar magnet of time period T is cut into four equal parts by cutting it perpendicular to both length and breadth. The time period of each part is

Moderate

A

T/4
B

T/16
C

T/32
D

T/2

Solution

$\begin{array}{rcl} MI, I & = & \frac{{ml}^{2}}{12}; \frac{I^{1}}{I} = \frac{1}{4} x \frac{1}{4}; \\ \frac{M^{1}}{M} & = & \frac{1}{4} \\ \frac{T}{T^{1}} & = & \sqrt{\frac{M^{1} I}{{MI}^{1}}} = \sqrt{4} = 2; \\ T^{1} & = & \frac{T}{2} \end{array}$

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