Question

Identify the correct statements from the following :
A. The charge on a body can have any value greater than the charge on an electron or proton.
B. Gauss's theorem is valid for a closed surface of any shape and for any general charge distribution.
C. The net flux through a closed surface due to a charge lying outside the closed surface is zero.
D. Gauss's theorem is applicable to any field which obeys the inverse square law
Choose the correct answer from the options given below:

• A. A, B and C only
• B. A, B and D only
• C. A, B, C and D
• D. B, C and D only

Hint:

Charge is quantised, so A is false. B, C and D are standard properties of Gauss's law.

Answer 1

The Correct Option is D

Step 1: Test Each Statement with a Known Fact:
A: Millikan's experiment showed every observed charge is a multiple of \(1.6\times10^{-19}\) C. A value like \(0.5e\) is never found, so A is false.

Step 2: Use the Flux Picture:
Gauss's law connects flux to enclosed charge only: \(\Phi = q_{in}/\varepsilon_0\). Nothing in it depends on the shape of the surface, so B is true. A charge outside adds nothing to \(q_{in}\), so its net flux is zero and C is true.

Step 3: Inverse Square Requirement:
For a point source, the flux through a sphere is \(E \cdot 4\pi r^2\). If \(E \propto 1/r^2\), this is constant for every radius. So the theorem works for any inverse square field, such as gravity as well. D is true.

Step 4: Conclusion:
The set of true statements is {B, C, D}. This is the fourth printed option.

Final Answer:
\[\boxed{\text{B, C and D only (option 4)}}\]