Ncert Exercises & Solutions

Q 1.18)

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

( Hint: Think of the square as one face of a cube with edge 10 cm)

Question 1.18

It can be considered that the charge is placed at the centre of a cube of edge 10 cm.

According to Gauss's theorem, the total electric flux is through all its six faces:

$ϕ_{Total} = \frac{q}{ε_{0}}$ $ϕ_{Total} = \frac{q}{ε_{0}}$
Hence, the electric flux through one face of the cube:
$ϕ = \frac{ϕ_{Total}}{6} = \frac{1}{6} \cdot \frac{q}{ε_{0}}$ $ϕ = \frac{ϕ_{Total}}{6} = \frac{1}{6} \cdot \frac{q}{ε_{0}}$

$q = 10 μC = 10 \times 10^{- 6} C$ $q = 10 μC = 10 \times 10^{- 6} C$
$\Rightarrow ϕ = \frac{1}{6} \cdot \frac{10 \times 10^{- 6}}{8 .854 \times 10^{- 12}}$ $\Rightarrow ϕ = \frac{1}{6} \cdot \frac{10 \times 10^{- 6}}{8 .854 \times 10^{- 12}}$
$= 1 .88 \times 10^{5} {Nm}^{2} C^{- 1}$ $= 1 .88 \times 10^{5} {Nm}^{2} C^{- 1}$

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