Question

El Electric potential of a uniformly charged solid sphere insultor Ur”) everywhere? Ē (r) = { ka ,ROR

Answer 1

Sol First we calculate the electric field for r > R and YER. for rer Let the charge enclosed by the sphere of radius r s é Applying Gauss's the arem, we get a $ Ē. ds = 451k Q' (In Cags system) E. 4582 = 45kQ' * E - keep Now, Now a Q = 4 rrug and Q = 4 x 239 : E = K () ; P<R for r>R. - Applying Gauss theorem, ffe. ds = 417kQ 1. E. 4772 = 45kQ . E=kQ ;r>R Scanned with CamScanner

field, Therefore, we get the electric Ě - j k l firme l a 2) ; rer Now we find the potential for r >R and r LR. for r>R The electric field for 'r yr is, E=kQ .: Potential. V = - Fedy E-ligheder Take V = ke; r R For rar for rar, the potential is, v=- Jite te - (eca) KQ CS Scanned wito CamScanner Ca sama 600 F Hoe [1- (2]

2 V = the Cape C) =kQ (2R²-p2 1 R3 :r<R v=) kQ; r>R ka (pretxa); rer Scanned with CamScanner