Question

The product of the total electric flux emanating from a closed surface enclosing a charge \( q \) in free space is (\( \epsilon_0 \) - electrical permittivity of free space):

• A. 1
• B. \( \frac{q}{\epsilon_0} \)
• C. \( q \)
• D. \( q\epsilon_0 \)
• E. \( \epsilon_0 \)

Hint:

Gauss's Law relates the total electric flux through a closed surface to the charge enclosed within the surface, using the permittivity of free space \( \epsilon_0 \).

Answer 1

The Correct Option is B

Gauss's Law states that the total electric flux \( \Phi_E \) through a closed surface is directly proportional to the charge enclosed within the surface. Mathematically, it is expressed as: \[ \Phi_E = \frac{q}{\epsilon_0} \] where: - \( \Phi_E \) is the total electric flux,
- \( q \) is the charge enclosed by the surface,
- \( \epsilon_0 \) is the permittivity of free space.
The product of the total electric flux and the permittivity of free space is given by: \[ \Phi_E \times \epsilon_0 = \frac{q}{\epsilon_0} \times \epsilon_0 = q \] Thus, the correct answer is \( \frac{q}{\epsilon_0} \).
Therefore, the correct answer is option (B), \( \frac{q}{\epsilon_0} \).