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Potential Energy of a Dipole in Uniform Electric Field

A spherical s...

Question

A spherical shell of radius $R_{1}$ with uniform charge $q$ is expanded to a radius $R_{2}$ . Find the work performed by the electric forces during the shell expansion from $R_{1}$ to radius $R_{2}$ .

\frac{q^{2}}{2 π ϵ_{0} n_{0}} (\frac{1}{R_{1}} - \frac{1}{R_{2}})

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\frac{q^{2}}{3 π ϵ_{0} n_{0}} (\frac{1}{R_{1}} - \frac{1}{R_{2}})

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\frac{q^{2}}{5 π ϵ_{0} n_{0}} (\frac{1}{R_{1}} - \frac{1}{R_{2}})

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\frac{q^{2}}{8 π ϵ_{0} n_{0}} (\frac{1}{R_{1}} - \frac{1}{R_{2}})

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Solution

The correct option is D $\frac{q^{2}}{8 π ϵ_{0} n_{0}} (\frac{1}{R_{1}} - \frac{1}{R_{2}})$
Spherical shell of radius $= R_{1}$
charge $= q$
work done $= W = q (V_{B} - V_{A})$
$V_{A} = \frac{K_{q}}{R_{1}}$
$V_{B} = \frac{K_{q}}{R_{2}}$
$W = q (\frac{K_{q}}{R_{1}} - \frac{K_{q}}{R_{2}})$
$= \frac{q^{2}}{8 π ϵ_{0} n_{0}} (\frac{1}{R_{1}} - \frac{1}{R_{2}})$ (Proved).

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Similar questions

Two concentric, thin metallic spherical shells of radii $R_{1}$ and $R_{2} (R_{1} > R_{2})$ bear charges $Q_{1}$ and $Q_{2}$ respectively. Then the potential at radius ‘r’ between $R_{1}$ and $R_{2}$ will be $\frac{1}{4 π ϵ_{0}}$ times

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A spherical shell of radius R1 with uniform charge q is expanded to a radius R2. Find the work performed by the electric forces during the shell expansion from R1 to radius R2.

The correct option is D q28πϵ0n0(1R1−1R2)Spherical shell of radius =R1charge =qwork done =W=q(VB−VA)VA=KqR1VB=KqR2W=q(KqR1−KqR2) =q28πϵ0n0(1R1−1R2) (Proved).

A spherical shell of radius $R_{1}$ with uniform charge $q$ is expanded to a radius $R_{2}$ . Find the work performed by the electric forces during the shell expansion from $R_{1}$ to radius $R_{2}$ .