An infinite line of charge with linear density λ1 = 7.9 μC/m is positioned along the axis of a thick insulating shell of inner radius a = 2.6 cm and outer radius b = 4.5 cm. The insulating shell is uniformly charged with a volume density of ρ = -658 μC/m3.
1) What is λ2, the linear charge density of the insulating shell?
Solution:
The shell is non conducting or made up of insulating material, thus, charge on shell will uniformly distribute in it's entire volume. Also, there is no charge redistribution occur on shell due to the line charge present at it's axis.
Thus,
Volume charge density = total charge / volume of the shell
\
Similarly, linear charge density = Total charge / length of the shell
Comparing above two we get,
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