The electric field at point p just outside the outer surface of a hollow spherical conductor of inner radius 10 cm and outer radius 20 cm has magnitude 459 n/c and is directed outward. when an unknown point charge q is introduced into the center of the sphere, the electric field at p is still directed outward but is now 181 n/c. (a) what is the net charge on and enclosed by the outer spherical surface before q is introduced?

Explanation:

Given:

Before introducing the charge Q,

Consider a Gaussian sphere of same radius as the outer radius of the shell, concentric with the given shell,

Applying Gauss' law over this surface,

where,

The directions of the area element and the electric field, both are directed outward the surface, therefore, .

The LHS of the equation of the Gauss' law is given as

is the surface area of the Gaussian sphere =

Therefore, using the equation of the Gauss' law,

It is the net charge enclosed by the outer surface before Q was introduced.

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