Question

The electric potential immediately outside a charged conducting sphere is 240 V, and 10.0 cm farther from the center of the sphere the potential is 140 V.

(a) Determine the radius of the sphere.

__________cm

(b) Determine the charge on the sphere.

__________nC

The electric potential immediately outside another charged conducting sphere is 270 V, and 10.0 cm farther from the center the magnitude of the electric field is 410 V/m.

(c) Determine all possible values for the radius of the sphere. (Enter your answers from smallest to largest. If only one value exists, enter "NONE" in the second answer blank.)

r1 =__________ cm

r2 =__________ cm

(d) Determine the charge on the sphere for each value of r. (If only one value exists, enter "NONE" in the second answer blank.)

q1 =__________ nC

q2 =__________ nC

Answer 1

a)

r = radius of sphere

Q = charge on sphere

V_s = electric potential at the surface = 240 Volts

V = electric potential at distance 10 cm = 140 volts

electric potential at the surface is given as

V_s = kQ/r

240 = kQ/r eq-1

electric potential at the 10 cm distance is given as

V = kQ/(r + 0.1)

140 = kQ/(r + 0.1) eq-2

dividing eq-1 by eq-2

240/140 = (r + 0.1)/r

r = 0.14 m = 14 cm

using eq-1

240 = kQ/r  

240 = (9 x 10⁹) Q/(0.14)  

Q = 3.7 x 10^-9 C = 3.7 nC