Capacitance of an isolated conducting sphere of radius R 1 becomes n times when it is enclosed by a concentric conducting sphere of radius R 2 connected to earth. The ratio of their radii R 2 R 1 is:

Step-by-step solution

Capacitance of isolated conducting sphere C = 4 π ε 0 R 1 By enclosing inside another sphere of radius R 2 , new capacitance C ' = 4 π ε 0 R 1 R 2 R 2 - R 1 Given: 4 π ε 0 R 1 R 2 R 2 - R 1 = n × 4 π ε 0 R 1 ⇒ R 2 R 2 - R 1 = n ⇒ R 2 R 1 R 2 R 1 - 1 = n ⇒ R 2 R 1 = n R 2 R 1 - n ⇒ R 2 R 1 = n n - 1