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A point charge +Q is placed just outside an imaginary hemispherical surface of radius R, positioned at the center of the flat circular face (just outside, along the axis). Which of the following statements is/are correct?

1. The circumference (rim) of the flat circular face is an equipotential curve.
2. The electric flux through the curved hemispherical surface is -(Q / (2*epsilon₀)) * (1 - 1/sqrt(2)).
3. The total electric flux through both the curved and flat surfaces is Q / epsilon₀.
4. The component of the electric field perpendicular to the flat surface is constant everywhere on the flat surface.

Correct answer: The circumference (rim) of the flat circular face is an equipotential curve.

Solution

Since +Q is outside the closed surface, Gauss's law gives zero total flux. The rim is equidistant from +Q so it is equipotential. The normal E-field on the flat disk is not uniform (it varies with radial distance from the center). The flux through the curved surface equals the negative of that through the flat disk.

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