Question

The capacitance of a spherical condenser whose inner surface is grounded is 1 microfarad if the spacing between the two spheres is 1 m then what is the radius of the outer sphere

Answer 1





Then ,since we know that for a cylindrical condenserC = 4πε0[1rin − 1rout] = 4πε0[1r1 − 1r1 + 0.001]1 × 10−6 =  4 × 3.14 ×8.854 ×10−12[1r1 − 1r1 + 0.001][1r1 − 1r1 + 0.001] = 4 × 3.14 ×8.854 ×10−121 × 10−6 [(r1 + 0.001) − r1]r1×(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