Question

A non-conducting sphere of radius R = 5 cm has its centre at the origin O of the coordinate system. It has a spherical cavity of radius r = 1 cm having its centre at (0, 3 cm). The solid material of the sphere has a uniform positive charge density `rho = 10^-6/pi` coulomb m^-3. The potential at point P is ______ volt. (4 cm, 0).

विकल्प

• 30.11

• 35.16

• 31.12

• 43.12

Answer 1

A non-conducting sphere of radius R = 5 cm has its centre at the origin O of the coordinate system. It has a spherical cavity of radius r = 1 cm having its centre at (0, 3 cm). The solid material of the sphere has a uniform positive charge density `rho = 10^-6/pi` coulomb m^-3. The potential at point P is 35.16 volts.

Explanation:

Assuming the given sphere is solid, calculate potential V₁ at P. However, because there is no charge in the cavity, potential V₂ due to the assumed charge in the cavity must be subtracted from V₁.

Charge on solid sphere = `4/3piR^3 xx rho`

= `5/3 xx 10^-10`c

Potential at P can be calculated, say V₁

V₂ = Potential due to cavity sphere

= `(4/3pir^3rho)/(4piε_0a)` = 0.24 V

Potential at P = V₁ – V₂ = 35.16 volt