A solid sphere of radius R is charged uniform | vedclass

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(C) The electrostatic potential at the center of a uniformly charged solid sphere of radius $R$ is given by $V_c = \frac{3}{2} \frac{kQ}{R}$.For a poi

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$R/3$

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(C) The electrostatic potential at the center of a uniformly charged solid sphere of radius $R$ is given by $V_c = \frac{3}{2} \frac{kQ}{R}$.For a point outside the sphere at a distance $x$ from the center (where $x > R$),the potential is $V(x) = \frac{kQ}{x}$.According to the problem,the potential at distance $x$ is half of the potential at the center:$V(x) = \frac{1}{2} V_c$$\frac{kQ}{x} = \frac{1}{2} \left( \frac{3}{2} \frac{kQ}{R} \right)$$\frac{1}{x} = \frac{3}{4R}$$x = \frac{4R}{3}$.The distance from the surface of the sphere is $d = x - R = \frac{4R}{3} - R = \frac{R}{3}$.

$A$ solid sphere of radius $R$ is charged uniformly. At what distance from its surface is the electrostatic potential half of the potential at the centre?

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