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 $3 \times 10^{-5} C / m ^{3} \cdot \varepsilon_{0}$ is the permittivity of free space in $C ^{2} / Nm ^{2}$. 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. $\frac{0.4 \pi \times 10^{-7}}{\varepsilon_{0}}$
• B. $\frac{0.8 \pi \times 10^{-7}}{\varepsilon_{0}}$
• C. $\frac{1.2 \pi \times 10^{-7}}{\varepsilon_{0}}$
• D. $\frac{1.6 \pi \times 10^{-7}}{\varepsilon_{0}}$

Answer 1

Answer: (D)

Electric flux through spherical surface
$=\frac{q_{\text {net enclosed }}}{\varepsilon_{0}}$
$=\frac{\text { Charge of shell }+\text { Charge of sphere }}{\varepsilon_{0}}$
$=\frac{1}{\varepsilon_{0}}\begin{bmatrix}4 \pi\left(0.06^{\frac{1}{2}}\right)^{2} \times(-10)^{-6} \\ + \frac{4}{3} \pi\left(0.01^{\frac{1}{3}}\right)^{3} \times 3 \times 10^{-5}\end{bmatrix}$
$=\frac{\pi}{\varepsilon_{0}}\left\{-0.24 \times 10^{-6}+0.39 \times 10^{-6}\right\}$
$=\frac{1.6 \pi \times 10^{-7}}{\varepsilon_{0}} V - m$