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Question

(A) The electric field $E$ inside a uniformly charged solid sphere at a distance $r$ from the center is given by $E = \frac{Q r}{4 \pi \varepsilon_0 R

Vedclass · Accepted Answer

$\frac{1}{2 \pi}\left[\frac{Q q}{4 \pi \varepsilon_0 R^3 m}\right]^{\frac{1}{2}}$

Vedclass · Answer

(A) The electric field $E$ inside a uniformly charged solid sphere at a distance $r$ from the center is given by $E = \frac{Q r}{4 \pi \varepsilon_0 R^3}$.Since the particle has a charge $-q$,the restoring force acting on it is $F = -qE = -\frac{Q q r}{4 \pi \varepsilon_0 R^3}$.This force is of the form $F = -kr$,where the force constant $k = \frac{Q q}{4 \pi \varepsilon_0 R^3}$.The frequency of oscillation $f$ is given by $f = \frac{1}{2 \pi} \sqrt{\frac{k}{m}}$.Substituting the value of $k$,we get $f = \frac{1}{2 \pi} \sqrt{\frac{Q q}{4 \pi \varepsilon_0 R^3 m}}$.

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