WBJEE · Physics · Electrostatics
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?
- A \(\rho \frac{x}{\varepsilon_{0}}\)
- B \(\rho \frac{x}{2 k \varepsilon_{0}}\)
- C \(\rho \frac{\mathrm{x}^{2}}{2 \mathrm{a} \varepsilon_{0}}\)
- D \(\rho \frac{\mathrm{x}^{2}}{2 \mathrm{k}}\)
Answer & Solution
Correct Answer
(B) \(\rho \frac{x}{2 k \varepsilon_{0}}\)
Step-by-step Solution
Detailed explanation
Hint: Using Gauss's Law \(\mathrm{E}(2 \pi \times \ell)=\frac{\rho\left(\pi \mathrm{X}^{2} \ell\right)}{\mathrm{k} \varepsilon_{0}} \quad \therefore \mathrm{E}=\frac{\rho \mathrm{x}}{2 \mathrm{k} \varepsilon_{0}}\)
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