Question

In the given diagram, there is a conducting sphere of radius $r_{1}$ which is surrounded by a dielectric of relative permittivity $\epsilon _{r}$ . If conducting sphere is given charge $q$ , then the surface density of polarization charges, on the outer surface of the dielectric layer, is

• A. $\frac{\varepsilon_{ r } q}{4 \pi r_{2}^{2}}$
• B. $\frac{q}{4 \pi \varepsilon_{ r } r_{2}^{2}}$
• C. $\frac{\left(\varepsilon_{ r }-1\right) q}{4 \pi r_{2}^{2}}$
• D. $\frac{\left(\varepsilon_{ r }-1\right) q}{4 \pi \varepsilon_{ r } r_{2}^{2}}$

Answer 1

Answer: (D)

Induced charge $=q\left(1-\frac{1}{\varepsilon_{ r }}\right)$
Surface density $=\frac{q\left(1-\frac{1}{\varepsilon_{ F }}\right)}{4 \pi r_{2}^{2}}=\frac{q\left(\varepsilon_{ r }-1\right)}{4 \pi \varepsilon_{ r } r_{2}^{2}}$