Cut Magnet!

Electricity and Magnetism Level 4

A magnet is cut in four equal parts by cutting it parallel to its length. What will be the time period of each part, if the time period of original magnet in the same field is T 0 T_0 ?

Submit your answer of ratio T Full magnet : T 1 4 t h Magnet T_{\text{Full magnet}} : T_{\frac{1}{4}^{th}\text{Magnet}} .


The answer is 1.41421.

Samara Simha Reddy by Samara Simha Reddy , 22, India

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1 solution

I 1 = I 4 and M 1 = M 2 . ∴ T 0 = 2 π I M B . ⟹ T 1 = 2 π I 1 M 1 B = 2 π I × 2 4 M × B ∴ T 1 T 0 = 1 2 ∴ T 1 = T 0 2 . ⟹ T initial : T final = T 0 T 0 2 = 2 ≈ 1.41421 \large \displaystyle I_1 = \frac{I}{4} \text{ and } M_1 = \frac{M}{2}.\\ \large \displaystyle \therefore T_0 = 2\pi \sqrt{\frac{I}{MB}}.\\ \large \displaystyle \implies T_1 = 2\pi\sqrt{\frac{I_1}{M_1 B}} = 2\pi \sqrt{\frac{I \times 2}{4M \times B}}\\ \large \displaystyle \therefore \frac{T_1}{T_0} = \frac{1}{\sqrt2}\\ \large \displaystyle \therefore T_1 = \frac{T_0}{\sqrt2}.\\ \large \displaystyle \implies T_{\text{initial}} : T_{\text{final}} = \frac{T_0}{\frac{T_0}{\sqrt2}} = \sqrt{2} \approx \color{#69047E}{\boxed{1.41421}}

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