Question

A metal sphere with radius R1 has a charge Q1. Take the electric potential to be zero at an infinite distance from the sphere.

Answer 1

Answer:

Part A :  E =   $\frac{1}{4\pi}$ε₀ Q₁/R₁² Volt/meter

Part B :  V =  $\frac{1}{4\pi}$ε₀ Q₁/R₁ Volt

Explanation:

Given that,

Charge distributed on the sphere is Q₁

The radius of sphere is R

₁

The electric potential at infinity is 0

Part A

The space around a charge in which its influence is felt is known in the electric field. The strength at any point inside the electric field is defined by the force experienced by a unit positive charge placed at that point.  

If a unit positive charge is placed at the surface it experiences a force according to the Coulomb law is given by

                          F = $\frac{1}{4\pi}$ε₀ Q₁/R₁²

Then the electric field at that point is

                                   E =  F/1

                            E =  $\frac{1}{4\pi}$ε₀ Q₁/R₁²  Volt/meter

Part B

The electric potential at a point is defined as the amount of work done in moving a unit positive charge from infinity to that point against electric forces.

Thus, the electric potential at the surface of the sphere of radius R₁ and charge distribution Q₁ is given by the relation

                           V =  $\frac{1}{4\pi}$ε₀ Q₁/R₁  Volt