A system consists of two spherical concentric shells made from conductive materi

Question

A system consists of two spherical concentric shells made from conductive materials. He first shell has an internal radius of 2cm and external radius of 4cm, while the second shell has an internal radius of 6cm and external radius of 9cm. The charges of the spherical shells are (a) internal cylindrical shell has a charge of 4 micro C (b) external cylindrical shell has a charge of -8 micro C. Calculate: (a) The electric field for the points at r = lcm. (b) The electric field for the points at r = 3cm. (c) The electric field for the points at r = 5cm. (d) The electric field for points at r-8cm. (e) The electric field for point at r = 11cm. (f) The electric flux through a cylinder with a radius of 12 cm and height of 20cm. (g) The distribution of charges on the internal and external surface of each shell. *Show al the steps and diagram

Explanation / Answer

consider a spherical gausean surfaqce at radius r
then from gauss law
electric field atr points in the spherical surface of the gaussean surface be E
then
E*4*pi*r^2 = qen/epsilon
qen is enclosed charge
epsilon is permittivity of free space
a) r = 1 cm
qen = 0
so E = 0 V/m
b) 3 cm
this is inside the first shell, which is a conductor
and electric field inside conductors is 0
so, E = 0
c) r = 5 cm
qen = chargfe on inner shell = -4*10^-6 C
E = kqen/r^2 = 8.98*10^9 * (-4*10^-6)/0.05^2 = 1.436*10^7 V/m
d) r = 8 cm
inside second shell so E = 0
e) r = 11 cm
q en = -4 - 8 = -12 micro C
E = 8.98*10^9*(-12*10^-6)/0.11^2 = 8.905*10^6 V/m
f) Flux = qin/epsilon = -12*10^-6*4*pi*8.98*10^9 = 1.354*10^6 Vm
g) inner shell
inner surface charge = 0
outer surtface charge = -4 micro C
outer shell
inner surface charge = 4 micro C
outer surface charge = -12 micro C

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