Question

A point charge causes an electric flux of \( -2 \times 10^4 \, \text{Nm}^2\text{C}^{-1} \) to pass through a spherical Gaussian surface of 8.0 cm radius, centered on the charge. The value of the point charge is:

• A. \( 17.7 \times 10^{-7} \, \text{C} \)
• B. \( 15.7 \times 10^{-7} \, \text{C} \)
• C. \( 17.7 \times 10^{-6} \, \text{C} \)
• D. \( 15.7 \times 10^{-6} \, \text{C} \)

Hint:

Gauss's law relates the electric flux through a surface to the charge enclosed by that surface. Be sure to use the correct value for the permittivity of free space (\( \epsilon_0 \)) in calculations.

Answer 1

The Correct Option is A

According to Gauss's law, the electric flux through a closed surface is related to the charge enclosed by the surface: \[ \Phi_E = \frac{q}{\epsilon_0} \] where \( \Phi_E \) is the electric flux, \( q \) is the charge, and \( \epsilon_0 \) is the permittivity of free space. Given that \( \Phi_E = -2 \times 10^4 \, \text{Nm}^2\text{C}^{-1} \) and the radius of the Gaussian surface is \( r = 8.0 \, \text{cm} \), we can solve for the charge \( q \) as: \[ q = \Phi_E \times \epsilon_0 = (-2 \times 10^4) \times (8.85 \times 10^{-12}) = 17.7 \times 10^{-7} \, \text{C} \]