First slide

Gauss's Law

Question

A uniformly charged conducting sphere of 2.4 m diameter has a surface charge density of 80.0 $μC / m^{2}$ . What is the total electric flux leaving the surface of the sphere?

Moderate

A

1.6 x 10⁸ Nm²/C
B

3.2 x 10⁸ Nm²/C
C

4.8 x 10⁸ Nm²/C
D

6.4 x 10⁸ Nm²/C

Solution

We know that charge on the sphere
= Density x Area
$\begin{array}{l} = 80 \times 10^{- 6} \times 4 π (1 .2)^{2} \\ = 1 .45 \times 10^{- 3} C \end{array}$
Therefore, the total electric flux leaving the surface of the sphere is
$ϕ = \frac{q}{ε_{0}} = \frac{1 .45 \times 10^{- 3}}{8 .86 \times 10^{- 12}} = 1 .6 \times 10^{8} {Nm}^{2} / C$

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