A thin ring of radius R has charge +Q uniformly distributed — JEE Physics
A thin ring of radius $R$ has charge $+Q$ uniformly distributed. A particle of mass $m$ and charge $+q$ is placed at the center. It is displaced slightly along the axis. Show it executes SHM and find the time period.
1 Answer
VAVidaara Admin
✓ Vidaara Team
✓ Accepted
· 1mo ago
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For displacement $x \ll R$, the restoring force from the ring's field:
$$F = -qE = -\frac{qQx}{4\pi\epsilon_0 R^3}$$
Comparing with $F = -kx$, we get $k = \dfrac{qQ}{4\pi\epsilon_0 R^3}$
$$T = 2\pi\sqrt{\frac{m}{k}} = 2\pi\sqrt{\frac{4\pi\epsilon_0 m R^3}{qQ}}$$
$$T = 2\pi\sqrt{\frac{4\pi\epsilon_0 m R^3}{qQ}}$$
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Discussion (2)
N
Thanks a ton, I was stuck on this exact problem for an hour.
DM
Is there a faster shortcut for this in the actual exam? Time is tight.