A metallic spherical shell has an inner radius of 5.80 cm and an outer radius of

Question

A metallic spherical shell has an inner radius of 5.80 cm and an outer radius of 9.00 cm . The surface charge density on the inner surface is -100 nC/m2 while the surface charge density on the outer surface is +100 nC/m2 . The image shows a cross section of the metallic shell.(Figure 1)

Part A

What is the strength of the electric field at point 4 cm from the center?

Part B

What is the direction of the electric field at point 4 cm from the center?

Part C

What is the strength of the electric field at point 8 cm from the center?

Part D

What is the direction of the electric field at point 8 cm from the center?'

Part E

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

Part F

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

Explanation / Answer

Surface area for inner sphere = 4**(5.8*10-2)2

Charge on inner surface = 4**(5.8*10-2)2 * - 100 nC = - 4.227 nC

Q = 4.227 nC

Charge on outer surface = q

q = 4**(9*10-2)2 * 100 nC = 10.18 nC

a) Electric field at r = 4 cm

E = kQ/r^2 = 9e9*4.227*10^-9/0.04/0.04

E = 23.78 kN/C

b) outside

c) Electric field at r = 8 cm

inside the metal there will be no electric field ( being a conductor)

E = 0

d) no direction

e) Electric field at r = 12 cm

E = kq/r^2 = 9e9*10.18e-9/0.12/0.12

E = 6.36 kN/C

f) outside

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