Question

A thin spherical shell encloses a concentric solid sphere. The radius of the shell is $(0.060{)}^{\frac{1}{2}}m$ and its surface charge density is $-10^{-6}C/m^2$. The radius of the solid sphere is $(0.01{)}^{\frac{1}{3}}m$ and its volumetric charge density is $3\times 10^{-5}C/m^3\cdot {\epsilon }_0$ is the permittivity of free space in $C^2/N{m}^2$. The electric flux through a spherical surface concentric with the spherical shell and of radius greater than that of the shell in $V-m$ is

• A. $\frac{0.4\pi \times 10^{-7}}{{\epsilon }_0}$
• B. $\frac{0.8\pi \times 10^{-7}}{{\epsilon }_0}$
• C. $\frac{1.2\pi \times 10^{-7}}{{\epsilon }_0}$
• D. $\frac{1.6\pi \times 10^{-7}}{{\epsilon }_0}$

Answer 1

Answer: (D)

Electric flux through spherical surface
$=\frac{q_{\text{net enclosed }}}{{\epsilon }_0}$
$=\frac{\text{ Charge of shell }+\text{ Charge of sphere }}{{\epsilon }_0}$
$=\frac{1}{{\epsilon }_0}\left[\begin{array}{c}4\pi {\left(0.06^{\frac{1}{2}}\right)}^2\times (-10{)}^{-6}\\ +\frac{4}{3}\pi {\left(0.01^{\frac{1}{3}}\right)}^3\times 3\times 10^{-5}\end{array}\right]$
$=\frac{\pi }{{\epsilon }_0}\left\{-0.24\times 10^{-6}+0.39\times 10^{-6}\right\}$
$=\frac{1.6\pi \times 10^{-7}}{{\epsilon }_0}V-m$