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A very long charged solid cylinder of radius 'a' contains a uniform charge density $\rho$. Dielectric constant of the material of the cylinder is $\mathrm{k}$. What will be the magnitude of electric field at a radial distance ' $x^{\prime}(x < a)$ from the axis of the cylinder?
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Verified Answer
The correct answer is:
$\rho \frac{x}{2 k \varepsilon_{0}}$
Hint:
Using Gauss's Law
$\mathrm{E}(2 \pi \times \ell)=\frac{\rho\left(\pi \mathrm{X}^{2} \ell\right)}{\mathrm{k} \varepsilon_{0}} \quad \therefore \mathrm{E}=\frac{\rho \mathrm{x}}{2 \mathrm{k} \varepsilon_{0}}$
Using Gauss's Law
$\mathrm{E}(2 \pi \times \ell)=\frac{\rho\left(\pi \mathrm{X}^{2} \ell\right)}{\mathrm{k} \varepsilon_{0}} \quad \therefore \mathrm{E}=\frac{\rho \mathrm{x}}{2 \mathrm{k} \varepsilon_{0}}$
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