Question

If a charge \( q \) is placed at the centre of a closed hemispherical non-conducting surface, the total flux passing through the flat surface would
 

• A. zero
• B. \( \frac{q}{2\epsilon_0} \)
• C. \( \frac{q}{4\epsilon_0} \)
• D. \( \frac{q}{2\pi\epsilon_0} \)

Hint:

When using Gauss's law, remember that the flux through a surface depends on the symmetry of the charge distribution. For spherical symmetry, the flux is distributed evenly across all surfaces.

Answer 1

The Correct Option is A

Step 1: According to Gauss's Law, the total electric flux \( \Phi_E \) through a closed surface is given by: \[ \Phi_E = \frac{q_{{enc}}}{\epsilon_0} \] where \( q_{{enc}} \) is the enclosed charge and \( \epsilon_0 \) is the permittivity of free space. 
Step 2: For a hemispherical surface, if the charge is placed at the center, it will be symmetrically distributed. The flux passing through the entire hemispherical surface will be \( \frac{q}{\epsilon_0} \). 
Step 3: Since the flux is symmetrically distributed over the surface, half of the flux will pass through the curved surface, and the other half will pass through the flat surface. 
Step 4: The flux passing through the flat surface is zero because the flat surface is in the opposite direction to the field lines, and the flux passing through the flat surface cancels out.