The electric field just outside the surface of a hollow conducting sphere of radius 20 cm has a magnitude of 500 n/c and is directed outward. an unknown charge q is introduced into the center of the sphere and it is noted that the electric field is still directed outward but has decreased to 100 n/c. what is the magnitude of the charge q?

To solve this problem it is necessary to apply the concepts related to Gauss's Law.

Gauss's law establishes that the flow of certain fields through a closed surface is proportional to the magnitude of the sources of that field inside the same surface.

Mathematically it can be expressed as,

Where

A = Surface area of Gaussian surface

Q = Charge enclosed by Gaussian surface

= Permittivity of free space

E = Electric Field

Our values are given as

Therefore replacing at our equation we can find Q,

Therefore the magnitude of the charge is

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