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Question 44

A point charge causes an electric flux of $$-2 \times 10^{4}\,\text{N m}^2 \text{C}^{-1}$$ to pass through a spherical Gaussian surface of 8.0 cm radius, centred on the charge. The value of the point charge is : (Given $$\varepsilon_0 = 8.85 \times 10^{-12}\,\text{C}^2 \text{N}^{-1} \text{m}^{-2}$$ )

By Gauss law,

$$\Phi=\frac{q}{\epsilon_0}$$

So

$$q=ϵ_0Φ$$

Given

$$\Phi=-2\times10^4$$

$$\epsilon_0=8.85\times10^{-12}$$

Thus

$$q=(8.85\times10^{-12})(-2\times10^4)$$

$$=-17.7\times10^{-8}$$

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