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A long coaxial cable (figure) carries a uniform volume charge density on the inner cylinder (radius a), and a uniform surface charge density of the outer cylindrical shell (radius b). This surface charge is negative and is of just the right magnitude that the cable as a whole is electrically neutral. Graph between $|E|$ and s (distance from the axis) is best represented by:

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answer is B.

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Detailed Solution

$\begin{array}{l} ∮ E \cdot da = E \cdot 2 πs \cdot ℓ = \frac{1}{ϵ_{0}} Q_{enc} = \frac{1}{ϵ_{0}} {ρπs}^{2} ℓ; \\ E = \frac{ρs}{2 \in_{0}} \hat{s} \end{array}$

$∮ E \cdot da = E \cdot 2 πs \cdot ℓ = \frac{1}{ϵ_{0}} Q_{enc} = \frac{1}{ϵ_{0}} {ρπa}^{2} ℓ; E = \frac{{ρa}^{2}}{2 \in_{0} s} \hat{s}$

$∮ E \cdot da = E \cdot 2 πs \cdot ℓ = \frac{1}{ϵ_{0}} Q_{enc} = 0; E = 0$

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