Question

Two metal spheres, each of radius 3.7 cm, have a center-to-center separation of 2.3 m. Sphere 1 has a charge of +1.1 × 10^-8 C; sphere 2 has a charge of -3.4 × 10^-8 C. Assume that the separation is large enough for us to assume that the charge on each sphere is uniformly distributed (the spheres do not affect each other). With V = 0 at infinity, calculate in volts (a) the potential at the point halfway between their centers and the potential on the surface of (b) sphere 1 and (c) sphere 2.

Answer 1

Given

two metal sphere of radius r1 = 3.7 cm = r2

separation of the spheres is r = 2.3 m , mid way bwtween them is , r/2 = 1.65 m

charge on sphere1 is q1 = 1.1*10^-8 C , q2 = -3.4*10^-8 C

a) half way between their centers is r/2 = 1.65 m

v1 = kq1/(r/2) = (9*10^9*1.1*10^-8)/(1.65) V = 60 V

v2 = kq2/(r/2) = -(9*10^9*3.4*10^-8)/(1.65) V = -185.45 V

net potential is V = v1+V2 = 60-185.45 V = -125.45 V

b) on the surfaceof the sphere 1 is  

v1 = kQ1/r = 9*10^9*1.1*10^-8 /(3.7*10^-2) V = 2675.6757 V

c) on sphere 2

v1 = kQ2/r = -9*10^9*3.4*10^-8 /(3.7*10^-2) V = -8270.270 V