Question

Two isolated sphereical conductors have radii 5 cm and 0 cm, espctively They have charges of 12muC and -3muC. Find the charges after they are connected by a conductng wire. Also find the common potential after resistribution.

Answer 1

The charges after conducting to the wire is q = 1.35 μC and the common potential is 1.37 x 10^6 Volts.

Explanation:

Initial potential v1 = kQr^1 v2 = kQr^2

Let q is the charge transferred and v is the common potential and charge transfer from one metal to other continuous until they both acquire the same potential.

V = K(Q−q) / r1 = k(Q+q) / r2

12 × 10^−6 − q / 5 = -3 × 10^−6  + q / 10

2.4 x 10^-6 - q = - 0.3 x 10^-6 + q

2.4 x 10^-6 + 0.3 x 10^-6 = q + q

2.7 x 10^-6 = 2 q

q = 2.7 / 2 μC

q = 1.35 μC

Common potential = V = 9 × 10^9 × (9 −1.35) × 10^−6 / 5 × 10^−2

V = 68.85 x 10^3 / 5 × 10^−2

V = 13.77 x 10^5 = 1377000 = 1.37 x 10^6 Volts

Hence the charges after conducting to the wire is q = 1.35 μC and the common potential is 1.37 x 10^6 Volts