Question

Suppose a conducting sphere of radius 40 cm has a charge of 5 mC and a mass of 2 kg. What is the electric potential at the center of the sphere? (Answer in MV) Assume that the electric potential is zero at infinity.

Answer 1

For a conducting sphere with charge +Q, the electric potential is given by:

V = Q/(4πε₀r)

V is the potential, Q is the charge, and r is the distance away from the center of the sphere.

Let's say the radius of the sphere is R. The electric field inside a charged conducting sphere is 0, therefore the voltage for any r greater than R is given by V = Q/(4πε₀r). But for any r less than R, V stays at a constant value equal to Q/(4πε₀R).

We are looking for the potential at the center of the sphere where r = 0, so we are looking for V = Q/(4πε₀R)

Given values:

Q = 5×10⁻³C

R = 40×10⁻²m

Plug in and solve for V:

V = 5×10⁻³/(4π(8.85×10⁻¹²)(40×10⁻²))

V = 112MV