Question

Identify the correct statements with regard to the application of Gauss's law in electrostatics. (A) Gauss's law is true only for spherical closed surfaces. (B) The Gaussian surface should not pass through any discrete charges. (C) The total electric flux through any closed surface is zero, if no charge is enclosed by the surface. (D) The charge in the vicinity of the surface must be zero. Choose the correct answer from the options given below:

• (B) only
• (A) and (D) only
• (B) and (C) only
• (A) and (C) only

Hint:

Remember: \[ \Phi_E=\oint \vec{E}\cdot d\vec{A} = \frac{Q_{\text{enclosed}}}{\varepsilon_0} \] Only the enclosed charge determines the net electric flux. Charges outside the Gaussian surface do not affect the total flux.

Answer 1

The Correct Option is C

Concept: Gauss's law states that \[ \oint \vec{E}\cdot d\vec{A} = \frac{Q_{\text{enclosed}}}{\varepsilon_0} \] The net electric flux through a closed surface depends only on the total charge enclosed by that surface.

Step 1: Check statement (A). Gauss's law is valid for every closed surface, irrespective of its shape. \[ \boxed{\text{Statement (A) is false.}} \]

Step 2: Check statement (B). A Gaussian surface should not pass through a discrete point charge because the electric field becomes undefined at the location of the charge. \[ \boxed{\text{Statement (B) is true.}} \]

Step 3: Check statement (C). If no charge is enclosed, \[ Q_{\text{enclosed}}=0 \] Therefore, \[ \oint \vec{E}\cdot d\vec{A}=0 \] Hence the net electric flux through the closed surface is zero. \[ \boxed{\text{Statement (C) is true.}} \]

Step 4: Check statement (D). Charges may exist outside or near the Gaussian surface. They can contribute to the electric field but not to the net enclosed charge. \[ \boxed{\text{Statement (D) is false.}} \]

Step 5: State the answer. The correct statements are \[ (B)\ \text{and}\ (C) \] \[ \boxed{ (B)\ \text{and}\ (C)\ \text{only} } \] Hence, the correct option is \[ \boxed{(C)} \]