A point charge + 10 μC is 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).

Let us assume that the charge q = ± 10 μC = 10^–5 C is placed at a distance of 5 cm from the square ABCD of each side 10 cm. The square ABCD can be considered as one of the six faces of a cubic Gaussian surface of each side 10 cm.
Now, the total electric flux through the faces of the cube as per Gaussian theorem
Let us assume that the charge q = ± 10 μC = 10–5 C is placed at
Therefore, the total electric flux through the square ABCD will be

$straight ϕ subscript straight E space equals space 1 over 6 cross times straight ϕ space equals space 1 over 6 cross times straight q over straight epsilon subscript 0 space space space space space space equals space 1 over 6 cross times fraction numerator 10 to the power of negative 5 end exponent over denominator 8.854 space cross times space 10 to the power of negative 12 end exponent end fraction space space space space space equals space 1.88 space cross times space 10 to the power of 5 space Nm squared space straight C to the power of negative 1 end exponent$

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