Question

A spherical capacitor contains a charge of 3.50 nC when connected to a potential difference of 250 V. If its plates are separated by vacuum and the inner radius of the outer shell is 4.00 cm. Calculate the capacitance. Calculate the radius of the inner sphere. Calculate the electric field just outside the surface of the inner sphere.

Answer 1

Part A: The capacitance of the spherical plate capacitor is given by, 3.50 nc(109) = 250 V =1.4x10-F 1 pF 10-12 F = 14.0 pF Part B: The capacitance of the spherical plate capacitor is given by, C-478,"' 14.0 pF = 4 45 (8.85x10c»'N•m*)r[ 4.00 cm (1 ) (4.00 cm 19 cm) - (14.0*10* Fy ( 4.00 cm (--(885*10* c*/N•m*)(400 cm (10 cm) 5.6x10-13 - 14.0x10-12 )r = (4.45 x10-12 ) (18.45 x10 ")5.6x10- r = 0.0304 m 100 cm 0.07m 1m =3.04 cm Part C: The electric field just outside the inner sphere is given by, (0x10° Nm? / C) 3.50 nc(1010) = 3.41x10NC