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A small particle of mass m and charge-q ...

A small particle of mass m and charge-q is placed at point `P` on the axis of uniformly chrarged ring and releases. If `R gtgt x`, the particle will undergo oscillations along the axis of symmetry with an angurlar frequency that isequal to-
.

A

`sqrt((qQ)/(4 pi varepsilon_(0) mR^(3)))`

B

`sqrt((qQ)/(4 pi varepsilon_(0) mR^(4)))`

C

`sqrt((qQ)/(4 pi varepsilon_(0) mR^(3)))`

D

`sqrt((qQ)/(4 pi varepsilon_(0) mR^(4)))`

Text Solution

Verified by Experts

The correct Answer is:
A
` E_p = (KQx)/((R^2 +x^2)^(3//2))`
` F_R =- qE =- 1/(4 pi in_0 ) (Qq x)/ ((R^2 +x^2)^(3//2))`

since ` R gt. X ` so `F-R =- 1/(4 pi in_0) (Qq)/R^3 .x`
Compare with ` F+R =- Kx, K= (Qq)/(4 pi in_0 R^3)`
` omega = sqrt K/m rArr omega = sqrt((Qq)/(4 pi in_0 mR^3))`.
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