Question

A hollow metal sphere has 5cm and 10cm inner and outer radii, respectively. The surface charge density on the inside surface is ?150nC/m2 . The surface charge density on the exterior surface is +150nC/m2 .

What is the strength of the electric field at point 12 cm from the center?

Answer 1

Given that,

ri = 5 cm

ro = 10 cm

inner surface charge density, 1 = -150 nC/m^2

2 = 150 nC/m^2

At r = 12 cm,

Charge on inner surface,

q2 = 4*pi*ri^2*1

q2 = 4*3.14*(0.05)^2*-150*10^(-9)

q2 = -4.71*10^(-9) C

Charge on outer surface,

q1 = 4*pi*ro^2*2

q1 = 4*3.14*(0.10)^2*150*10^(-9) = 18.84*10^(-9) C

Net charge within gaussian surface,

q = -4.71*10^(-9) + 4.71*10^(-9) + 18.84*10^(-9) C

Electric field is,

E = kq / ro^2

E = 9*10^9*18.84*10^(-9) / (0.10)^2

E = 16956 N/C