Question

A charge of 145 µC is at the center of a cube of edge 60.0 cm. No other charges are nearby. (a) Find the flux through each face of the cube. N · m2/C (b) Find the flux through the whole surface of the cube. N · m2/C (c) Would your answers to parts (a) or (b) change if the charge were not at the center? (a) would change. (b) would change. Both (a) and (b) would change. Neither would change.

Answer 1

Explanation:

Given that,

Charge, $q=145\ \mu C$

Edge of the cube, $a=60\ cm=0.6\ m$

(a) The Gauss law gives the relation between the charge and the electric field. Mathematically it is given by :

$\phi=\dfrac{q_{encl}}{\epsilon_o}$

As there are 6 faces of a cube. It will share equal amount of flux. So,

$\phi=\dfrac{q_{encl}}{6\epsilon_o}$

$\phi=\dfrac{145\times 10^{-6}}{6\times 8.85\times 10^{-12}}$

$\phi=2.73\times 10^6\ Nm^2/C$

(b) For the whole surface, the flux is given by :

$\phi=\dfrac{q_{encl}}{\epsilon_o}$

$\phi=\dfrac{145\times 10^{-6}}{8.85\times 10^{-12}}$

$\phi=1.63\times 10^7\ Nm^2/C$

(c) If the charge is not present at the center of the cube, it  will present on another faces. As a result, the net charge doesn't change. So, the electric flux in part (b) doesn't change.

Also, if the charge is not at the center, the distribution of electric field is not uniform in each faces. Hence, the flux in part (a) changes.