Question

A spherical cavity of Radius R/2 is drilled in the centre of a plastic sphere of radius R and electric permittivity ε charged with a charge density ρ. Assuming the object sits in a vacuum and that the electric potential at infinity is zero, calculate the electric potential in the centre of the sphere.

Answer 1

The electric potential in the centres of the sphere is E  = Kq / (R/2) + Kq' / R

Explanation:

• The respective charges on the shell are q and q-
• The system is shown in the figure.
• Let x be the distance between the centres of the object.

Then for

X > R

Electrical potential is given as:

E = K(q + q ' ) / x

For R / 2 < x < R

Electric potential:

Kq / x + Kq' / R

For x < R/2  Electric potential = Kq / (R/2) + Kq' / R

Thus the electric potential in the centres of the sphere is E  = Kq / (R/2) + Kq' / R.

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