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Question: If a small sphere of mass m and charge q is hanged from a silk thread at an angle q with the surface...

If a small sphere of mass m and charge q is hanged from a silk thread at an angle q with the surface of a vertical charged conducting plate, then for equilibrium of sphere the surface charge density of the plate-

A

ε0mgtan⁡θq\frac{\varepsilon_{0}mg\tan\theta}{q}

B

ε02mgtan⁡θq\frac{\varepsilon_{0}2mg\tan\theta}{q}

C

e0 mg q tan q

D

ε0mgtan⁡θ3q\frac{\varepsilon_{0}mg\tan\theta}{3q}

Answer

ε02mgtan⁡θq\frac{\varepsilon_{0}2mg\tan\theta}{q}

Explanation

Solution

T sin q = qE …(1)

T cos q = mg …(2)

tan q = = qσ2ε0mg\frac { \mathrm { q } \sigma } { 2 \varepsilon _ { 0 } \mathrm { mg } }

s = 2ε0mgtan⁡θq\frac { 2 \varepsilon _ { 0 } \mathrm { mg } \tan \theta } { \mathrm { q } }