devarshi-dt-logo

Question:

Let P(r) = Q/πR4r be the charge density distribution for a solid sphere of radius R and total charge Q. For a point p1 inside the sphere at distance r1 from the centre of sphere, the magnitude of electric field is?

0

Qr12/4πϵ0R4

Q/4πϵ0r12

Qr12/3πϵ0R4

Solution:

Consider a differential thickness dr at a radius r.
We get the area for this differential thickness as
dA = 4πr2 dr
Thus we get the electric field at this point as
dE = k dQ/r12
or
dE = 1/4πϵo (Q/πR4)r (4πr2 dr) /r12
E = Q/4πϵ0r12 (1/R4)∫r=0r1 4πr3 dr = Qr12/4πϵ0R4