1. Tardigrade
  2. Question
  3. Physics
  4. 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 φE. Three additional charges are now added along the x axis: −3q at x=-(R/2), +5q at x=(R/2) and 4q at x=(3R/2), The flux through S is now

Question Error Report

Thank you for reporting, we will resolve it shortly

Back to Question

Q. 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 $\phi_{E}$. 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

UPSEEUPSEE 2016

Solution:

According to Gauss law, charge $=+q$
Electric flux, $\phi_{E}=\frac{q_{\text {inside }}}{\epsilon_{0}}=\frac{q_{0}}{\epsilon_{0}}$
Total charge inside the spherical Gaussian surface of radius $R$ is
$q_{\text {inside }} =(-3 q)+5 q +q$
$=-3 q+6 q$
$=3 q$
$\therefore $ Flux through $S$
$\phi=\frac{3 q}{\epsilon_{0}}=3 \phi_{E}$