The capacitance of a spherical condenser is 1μF If the spacing between the two spheres is 1 mm, then - Physics - Electric Charges And Fields

Question

The capacitance of a spherical condenser is 1μF If the spacing
between the two spheres is 1 mm, then the radius of the outer
sphere is : (1) 30 cm (2) 6 m (3) 5 cm (4) 3 m

Satyendra Singh · Accepted Answer

Then ,since we know that for a cylindrical condenserC = 4πε01rin - 1rout = 4πε01r1 - 1r1 + 0
0011 × 10-6 =  4 × 3
14 ×8
854 ×10-121r1 - 1r1 + 0
0011r1 - 1r1 + 0
001 = 4 × 3 14 ×8
854 ×10-121 × 10-6 r1 + 0
001 - r1r1×r1 + 0
001 = 4 × 3 14 ×8
854 ×10-6r1×r1 + 0
001 = 4 × 3 14 ×8
854 ×10-60 001r1×r1 + 0
001 = 4 × 3 14 ×8
854 ×10-3r12 + 0
001r1  - 4 × 3 14 ×8
854 ×10-3 = 0r12 + 0
001r1  - 0 1112 = 0r1 = 0
333 m or,r1 = -334 msince it cannot be negative,Therefore, radius of outer sphere = r1 + 0
001router = 0 334mor  r1 = 33
4 cm Therefore, option (1) is the most appropriate option

The capacitance of a spherical condenser is 1μF. If the spacing between the two spheres is 1 mm, then the radius of the outer sphere is : (1) 30 cm (2) 6 m (3) 5 cm (4) 3 m