IIT JEE , AIEEE Forum - Physics , Electricity

umang

What is the potential at the centre of a uniformly charged sphere of radius R and charge Q (uniformply distributed) ???

further , find the potential at a distance 'r' from the centre of the sphere .

I know the answer , but not the method to find it .

Pls reply with a detailed solution .

Thanks !!!!!

subs

ur ans will depend wether the sphere is a conductor or not!!!

plz mention dat!!!

Mr.IITIAN007

Yes your answer will depend upon the conductance and non-conductance of the sphere.

iitkgp_bipin

If it is non-conducting :

Assume a Gaussian surface of radius r.

If r < R the charged enclosed , q = Qr³/R³
Hence electric field , E₁ = (q/

₀A) = (Qr³/R³)/(4

r²

₀) = kQr/R³

If r > R the charged enclosed is Q.
Hence electric field , E₂ = kQ/r²

where k = (1/4

₀)

Since the solid sphere is being charged from bringing the charge from infinite distance , hence to find the electric potential we have to integrate the electric field from infinity to r.

Hence if r < R :

V = _[R]

^[r] E₁dr + _[-infinity]

^[R] E₂dr

= _[R]

^[r] (-kQ/R³)r.dr + _[-infinity]

^[R] (-kQ/r²)dr

= (kQ/2R)(3 - r²/R²)

If the sphere is conducting one :

Electric potential remains constant inside with a value = kQ/R

umang

Sir ,

some parts of ur solution are not visible !

Pls help !

I understood some part of it

Ask & Discuss Questions with Community & Experts