Question

A uniformly charged conducting sphere of diameter $1.2m$ has a surface charge density of $8.1\mu C/m^2$. Find the total electric flux leaving the surface of the sphere.

• A. $4.1\times 10^{6}N-m^2/C$
• B. $1.3\times 10^{4}N-m^2/C$
• C. $-4.1\times 10^{6}N-m^2/C$
• D. Zero

Answer 1

Answer: (A)

The given, $R=0.6m$,
${\epsilon }_0=8.85\times 10^{-12}{C}^2{N}^{-1}{m}^{-2}$
$\sigma =8.1\times 10^{-6}C/m^2$
${\varphi }_E=?$
The change on the sphere $q=4\pi R^2.\sigma$
$=4\times 3.14\times (0.6{)}^2\times 8.1\times 10^{-6}$
$=36.62\times 10^{-6}C$
The total electric flux ${\varphi }_E=\frac{q}{{\epsilon }_0}$
$=\frac{36.62\times 10^{-6}}{8.85\times 10^{-12}}$
$=\frac{36.62\times 10^6}{8.85}$
$=4.13\times 10^{6}N-m^2/C$