First slide

Gauss's Law

Question

A point charge +10 $μC$ is a distance 5cm directly above the centre of a square of side10 cm ,as shown in the figure. What is the magnitude of the electric flux through the square?

Moderate

A

$1.2 \times 10^{5} {Nm}^{2} / C$
B

$1.9 \times 10^{5} {Nm}^{2} / C$
C

$3.2 \times 10^{5} {Nm}^{2} / C$
D

$4.2 \times 10^{5} {Nm}^{2} / C$

Solution

It is given that a point charge +10 $μC$ is located at a distance 5 cm directly above the centre of a square of side 10 cm. Let us consider this to be a square of sides A B C D and let this be considered as one of the faces of the cube of side 10 cm. Therefore, from Gaussian theorem, the total electric flux through all six faces of the cube is given by
$ϕ = \frac{q}{ε_{0}}$
Hence, now, the flux through the square of side A B C D is obtained as
$\begin{array}{l} ϕ = \frac{1}{6} (\frac{q}{ε_{0}}) = \frac{1}{6} (\frac{10 \times 10^{- 6}}{8 .854 \times 10^{- 12}}) \\ = 1 .88 \times 10^{5} {Nm}^{2} / C \approx 1 .9 \times 10^{5} {Nm}^{2} / C \end{array}$

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