Question

A charge of 12.6 µC is at the geometric center of a cube. What is the electric flux through one of the faces? The permittivity of a vacuum is 8.85419 × 10−12 C 2 /N · m2 . Answer in units of N · m2 /C.

Answer 1

Answer:$\phi =2.37\times 10^5\ Nm^2/C$

Explanation:

Given

Magnitude of charge $q=12.6\ \mu C$

According to Gauss law net flux of an Electric field through a Gaussian surface is equal to one by epsilon times the charge enclosed

We know cube has six faces which are symmetrical about center

Total Flux$=\frac{q}{\epsilon _0}$

Due to symmetry

Flux through a single face $\phi =\frac{q}{6\epsilon _0}$

$\phi =\frac{12.6\times 10^{-6}}{6\times 8.85\times 10^{-12}}$

$\phi =2.37\times 10^5\ Nm^2/C$

Answer 2

Answer:

2.37 x 10^5 Nm²/C

Explanation:

charge, q = 12.6 micro Coulomb

ε0 = 8.85419 x 10^-12 C²/Nm²

According to gauss's theorem, the flux linked with the cube is

Ф = q / ε0

Flux linked with one face of the cube

Ф = q / 6ε0

$\phi= \frac{12.6\times 10^{-6}}{6\times 8.8541\times 10^{-12}}$

Ф = 2.37 x 10^5 Nm²/C