If a small sphere of mass m and charge q is hung from a silk thread at an angle θ with the surface of a vertical charged conducting plate, then for equilibrium of sphere, the surface charge density of the plate is
A
ϵ0(mgq)tanθ
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B
ϵ0(2mgq)tanθ
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C
ϵ0(mgq)tanθ
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D
ϵ0(mg3q)tanθ
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Solution
The correct option is Bϵ0(2mgq)tanθ There will be two components of the tension. Tcosθ=mg Tsinθ=electricforce Tsinθ=qE where E is the electric field due to the plate. tanθ=qEmg E=mgtanθqσϵ0=mgtanθqσ=mgϵ0tanθq this is the surface charge density of the sphere