Question

A uniformly charged conducting sphere of diameter $1.2 \,m$ 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, $R=0.6 m$,
$\varepsilon_{0}=8.85 \times 10^{-12} C^{2} N^{-1} m^{-2}$
$\sigma=8.1 \times 10^{-6} C / m^{2}$
$\phi_{E}=?$
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 $\phi_{E}=\frac{q}{\varepsilon_{0}}$
$=\frac{36.62 \times 10^{-6}}{8.85 \times 10^{-12}} $
$=\frac{36.62 \times 10^{6}}{8.85}$
$=4.13 \times 10^{6} \,N - m ^{2} / C$