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 center?

Question

A solid sphere of radius R is charged uniformly- At what distance from its surface is the electrostatic potential half of the potential the center-

Toppr Admin · Accepted Answer

-Potential at the center-of sphere is Vc-32kQR-Potential at some-distance x from center -KQx-kQx-12-32kQR- or x-4R-3-Distance from surface-is x-x2212-R-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 center?

Potential at the center of sphere is Vc=32kQR Potential at some distance x from center =KQx kQx=12(32kQR) or x=4R/3 Distance from surface is x−R=R/3

Potential at the center of sphere is $V_{c} = \frac{3}{2} \frac{k Q}{R}$

Potential at some distance x from center $= \frac{K Q}{x}$

$\frac{k Q}{x} = \frac{1}{2} (\frac{3}{2} \frac{k Q}{R})$ or $x = 4 R / 3$

Distance from surface is $x - R = R / 3$