Solveeit Logo
Login

Question

Physics Question on electrostatic potential and capacitance

A spherical conductor of radius 12 cm has a charge of 1.6 × 10–7C distributed uniformly on its surface. What is the electric field ?

  1. inside the sphere
  2. just outside the sphere
  3. at a point 18 cm from the centre of the sphere?
Answer

(a) Radius of the spherical conductor, r = 12 cm = 0.12 m Charge is uniformly distributed over the conductor, q = 1.6 × 10−7 C Electric field inside a spherical conductor is zero. This is because if there is field inside the conductor, then charges will move to neutralize it.

(b) Electric field E just outside the conductor is given by the relation,

E=14πεº.qr2E = \frac{1}{4πεº} . \frac{q}{r^2}

Where, εo = Permittivity of free space and 14πεo\frac{1}{4πε_o} = 9 × 109 Nm2 C-2

Therefore, E=9×109×1.6×10−7(0.12)2=105NC−1E = \frac{9×10^9×1.6×10-7}{( 0.12)^2} =10^5NC^{-1}

Therefore, the electric field just outside the sphere is 105 NC-1.

(c) Electric field at a point 18 m from the centre of the sphere = E1

Distance of the point from the centre, d = 18 cm = 0.18 m

E1=14πεo.qd2=9×109×1.6×10−7(1.8×10−2)2=4.4×104NC−1E_1 = \frac{1}{4πε_o}.\frac{q}{d_2} = \frac{9×109×1.6×10-7}{(1.8×10-2)2}=4.4×10^4 NC^{-1}

Therefore, the electric field at a point 18 cm from the centre of the sphere is 4.4 × 104 NC-1 .