Question

A spherical capacitor is formed from two concentric sphericalconducting shells separated by vacuum. The inner sphere has radius10.0 centimeters, and the separation between the spheres is 1.50centimeters. The magnitude of the charge on each sphere is 3.30nanocoulombs.1)What is the magnitude of the potential difference DeltaV between the two spheres?2)What is the electric-field energy stored in the capacitor?

Answer 1

Answer:

Δ V = 38.74 V, W= 6.39 × 10 ⁻⁸ J

Explanation:

Given: Let inner Sphere Radius r1 = 10.0 cm = 0.1 m

separation d = 1.50 cm = 0.015 m

so the radius of outer sphere will be 0.1 + 0.015 = 0.115 m =r2

charge Q = 3.30 nC= 3.30 × 10 ⁻⁹ C

K= 9.0 x 10⁹ N • m² / C²

To Find: Δ V= ? and W=?

Solution:

1) we know that   Δ V = K Q / (1/r1 - 1/r2)

Δ V = 9.0 x 10⁹ N • m² / C² × 3.30 × 10 ⁻⁹ C / (1/0.1 - 1/0.115)

Δ V = 38.74 V

2) W = VQ/2    

W=   1980 V  × 3.30 × 10 ⁻⁹ C /2

W= 6.39 × 10 ⁻⁸ J