Question 282 of 311

Two charges of $5Q$ and $-2Q$ are situated at the points $(3a,0)$ and $(-5a,0)$ respectively. The electric flux through a sphere of radius $4a$ having centre at origin is:

A$\dfrac{2Q}{{\epsilon }_{0}}$B$\dfrac{5Q}{{\epsilon }_{0}}$C$\dfrac{7Q}{{\epsilon }_{0}}$D$\dfrac{3Q}{{\epsilon }_{0}}$

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Answer: (B) $\dfrac{5Q}{{\epsilon }_{0}}$

As can be seen from the figure above, only the $5Q$ charge is inside the spherical region.
The formula to calculate the flux through the surface is given by
$\phi =\dfrac{{q}_{enc}}{{\epsilon }_{0}}...\left(1\right)$
From equation $(1)$, the flux through the given surface can be calculated as follows:
$\phi =\dfrac{5Q}{{\epsilon }_{0}}$