Question

An imaginary, closed spherical surface $S$ of radius $R$ is centered on the origin. A positive charge $+q$ is originally at the origin and electric flux through the surface is ${\varphi }_E$. Three additional charges are now added along the x axis: $-3q$ at $x=-\frac{R}{2},+5q$ at $x=\frac{R}{2}$ and $4q$ at $x=\frac{3R}{2}$, The flux through S is now

• A. $3{\varphi }_E$
• B. $4{\varphi }_E$
• C. $6{\varphi }_E$
• D. $7{\varphi }_E$

Answer 1

Answer: (A)

According to Gauss law, charge $=+q$
Electric flux, ${\varphi }_E=\frac{q_{\text{inside }}}{{ϵ}_0}=\frac{q_0}{{ϵ}_0}$
Total charge inside the spherical Gaussian surface of radius $R$ is
$q_{\text{inside }}=(-3q)+5q+q$
$=-3q+6q$
$=3q$
$\therefore$ Flux through $S$
$\varphi =\frac{3q}{{ϵ}_0}=3{\varphi }_E$