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QPages 141-142: Q8: HC Verma: Concepts of Physics - Volume 2 Gauss's Law Pages 141-142: Q8 Solution: A charge Q is placed at the centre of an imaginary…

⚠️ Common Exam Traps & Conceptual Pitfalls

Students often apply Gauss’s law directly to the open hemispherical surface, forgetting that the law is valid only for closed surfaces. To use it, you must add the flat circular face to form a closed Gaussian surface and then show that the flux through that face is zero (field is parallel to the plane) before concluding the curved part carries $\frac{Q}{2\epsilon_0}$.

A charge Q is placed at the centre of an imaginary hemispherical surface. Using symmetry arguments and Gauss's Law, find the flux of the electric field due to this charge through the surface of the hemisphere in the following figure.

Step-by-Step Verified Solution

**Answer:** Flux = Q2ϵ0\frac{Q}{2\epsilon_0}. **Step-by-Step Explanation:** The charge Q is at the centre of a hemisphere. The flux through the curved surface of the hemisphere equals half the total flux through a full sphere (since the flat circular surface has zero flux if the charge is at the centre and the surface is perpendicular to the field). Total flux through full sphere = Q/ϵ0Q/\epsilon_0. Flux through hemisphere = Q2ϵ0\frac{Q}{2\epsilon_0} .

All Questions in this Chapter

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