A and C are concentric conducting spherical s | vedclass

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Question

(C) The electric field at a distance $r$ from the center,where $r > b$,is the same as that of a point charge $Q$ at the center,because the dielectric

Vedclass · Accepted Answer

$\frac{Q}{4\pi \varepsilon _0 b}$

Vedclass · Answer

(C) The electric field at a distance $r$ from the center,where $r > b$,is the same as that of a point charge $Q$ at the center,because the dielectric shell is spherically symmetric and the total charge enclosed by a Gaussian surface of radius $r > b$ is $Q$.Using Gauss's Law for dielectrics,the electric field $E$ for $r > b$ is given by $E = \frac{1}{4\pi \varepsilon _0} \frac{Q}{r^2}$.The potential $V$ at a distance $b$ is calculated by integrating the electric field from infinity to $b$:$V = -\int_{\infty}^{b} E \cdot dr = \int_{b}^{\infty} \frac{1}{4\pi \varepsilon _0} \frac{Q}{r^2} dr = \frac{Q}{4\pi \varepsilon _0} \left[ -\frac{1}{r} \right]_{b}^{\infty} = \frac{Q}{4\pi \varepsilon _0 b}$.Thus,the dielectric does not affect the potential at points outside the dielectric shell.

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