Inside an infinitely long circular cylinder charged uniformly with volume density $ρ$ there is a circular cylindrical cavity. The distance between the axis of the cylinder and the cavity is equal to a. Find the electric field strength E inside the cavity. The permittivity us assumed to be equal to unity.

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$E = \frac{aρ}{ε_{0}} \bar{a}$ is directed toword the axis of cavity

$E = \frac{ρ}{3 ε_{0}} \bar{a}$ is directed away from the axis of cavity

$E = \frac{aρ}{3 ε_{0}} \bar{a}$ is directed away from the axis of cavity

$E = \frac{aρ}{2 ε_{0}} \bar{a}$ is directed toword the axis of cavity.

answer is D.

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Detailed Solution

For along cylinder $\Rightarrow E = \frac{ρr}{2 \in_{0}} where r \leq R$ and $E = \frac{{ρR}^{2}}{2 E_{0} r}$ where r $\geq$ R

$\begin{array}{l} E_{p} = \frac{ρ \bar{r}}{2 E_{0}} - \frac{ρb}{2 E_{0}} \\ \Rightarrow E_{ρ} = \frac{ρ}{2 ϵ_{0}} (\bar{r} - \bar{b}) \\ E_{p} = \frac{ρa}{2 ε_{0}} \end{array}$

( $∵$ By addition law of vector)

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