Question
Sun June 17, 2012

State Gauss's law in electrostatics.Consider an overall neutral sphere of radius R.This sphere has a point charge,+Q,at its centre and this positive charge is surrounded by a uniform density ro of negative charge up to a radius R.Use Gauss's law to obtain expression for the electric field,of this sphere,at a point distance r,from its centre where (a)r is less than R (b) r is greater than R. show that these two expressions give identical results,for the electric field at r=R.

Sun June 17, 2012
Guass law can be stated as:
Electric flux through a closed surface S
= q/?

q = total charge enclosed by S.

Since the total charge in the sphere is 0, we can say that,

1. For r<=R
Thus for r=R,
QT =0

2. for r>R i.e outside the sphere clearly, QT =0
From guass law,
electric flux,? = QT /?
andelectric field,
E=?/4?r2

Clearly we can see that electric field on the surface and outside it are equal i.e 0.

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