Question

Gauss’s law states that the electric flux through a closed surface is

• A. proportional to the charge enclosed
• B. inversely proportional to the charge enclosed
• C. zero
• D. proportional to the square of the charge enclosed

Hint:

Gauss’s law links electric flux and charge enclosed. No square or inverse relations exist in its basic form.

Answer 1

The Correct Option is A

Step 1: Gauss’s Law.
Gauss’s law states that the total electric flux through a closed surface is directly proportional to the total charge enclosed within the surface. It is mathematically expressed as: \[ \Phi_E = \frac{Q_{\text{enc}}}{\epsilon_0} \] where \(\Phi_E\) is the electric flux, \(Q_{\text{enc}}\) is the charge enclosed, and \(\epsilon_0\) is the permittivity of free space.
Step 2: Analyze options.
- (A) Proportional to the charge enclosed: Correct. Gauss's law directly relates the electric flux to the enclosed charge.
- (B) Inversely proportional to the charge enclosed: Incorrect. The flux increases with the charge enclosed, not inversely.
- (C) Zero: Incorrect. The flux is not necessarily zero unless the charge enclosed is zero.
- (D) Proportional to the square of the charge enclosed: Incorrect. There is no square relation in Gauss’s law; the flux is directly proportional to the charge.
Step 3: Conclusion.
Gauss's law indicates that the electric flux is proportional to the charge enclosed.