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  4. Figure shows a charge q placed at the centre of a hemisphere. A second charge Q is placed at one of the positions A, B, C and D. In which position(s) of this second charge, the flux of the electric field through the hemisphere remains unchanged?

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Q. Figure shows a charge q placed at the centre of a hemisphere. A second charge Q is placed at one of the positions A, B, C and D. In which position(s) of this second charge, the flux of the electric field through the hemisphere remains unchanged?Physics Question Image

Electric Charges and Fields

Solution:

By Gauss's law, flux $\phi=\oint \vec{E} \cdot \hat{n} d S$
For charge at $A$ and $C$, the flux through the flat circular base will be zero
because $\vec{E}$ and $\hat{n}$ are perpendicular to each other.
Thus the flux through the hemisphere will be unchanged when charge $Q$ at $A$ and $C$.