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Q.

A long cylindrical insulating shell of inner radius a and outer radius b has a uniform volumetric charge density $ρ$ . A line of uniform linear charge density $λ$ is placed on the axis of the shell. If E is the electric field intensity at a distance r from the axes, choose the correct option(s).

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a

For $r < a, E = \frac{λ}{2 π r ε_{0}}$

b

For $a < r < b, E = \frac{λ + ρ π (r^{2} - a^{2})}{2 π r ε_{0}}$

c

For $r > b, E = \frac{λ + ρ π (b^{2} - a^{2})}{2 π r ε_{0}}$

d

For $r > b, E = \frac{λ - ρ π (b^{2} - a^{2})}{2 π r ε_{0}}$

answer is A, B, C.

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Detailed Solution

$\int \bar{E} . \bar{d s} = \frac{q_{e n c l o s e d}}{\in_{0}}$

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A long cylindrical insulating shell of inner radius a and outer radius b has a uniform volumetric charge density ρ. A line of uniform linear charge density λ is placed on the axis of the shell. If E is the electric field intensity at a distance r from the axes, choose the correct option(s).