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# a solid sphere of radius r is charged uniformly.at what distance from it surface electric potential is half of that of at its centre.ans:r/3

147 Points
11 years ago

Dear shefali

we know potential outside the sphere is V1 = kQ/x     where x is the distance from the center x>r

and potential inside the sphere V1 = kQ/2r [3-x2/r2]

for center put x=0  Vo = 3kQ/2r

condition given is V1 = Vo/2

kQ/x  = (3kQ/2r)/2

x=4r/3

distance from the surface is  =x-r

= 4r/3 -r =r/3

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askIITians Faculty 629 Points
one year ago
Hello student
For a spherically charged body with radius, R
The electic potential inside the sphere at its center is given by, V = 3kQ/2R
The electric potential at a distance r from the center of the sphere( r > R), Vr = kQ/r

Given, Vr = V/2
kQ/r = 3kQ/4R
hence, r = 4R/3

Hence distance from surface of sphere = r – R
= R/3

Regards,
Kushagra