Question

Statement A. The electric field generated from Gauss's law is path-independent.

Statement B: The electric field generated due to a changing magnetic flux is also path-independent.

Question: Which of the above statements are correct?

• A. Only A is correct.
• B. Only B is correct.
• C. Both A and B are correct.
• D. Neither A nor B is correct.

Answer 1

Answer: (A)

Only Statement A is correct.

Answer 2

Statement A refers to the electrostatic field, which is conservative, meaning the work done by the field (and thus the line integral) is path-independent. Statement B refers to the induced electric field due to changing magnetic flux (Faraday's law), which is non-conservative, meaning the line integral around a closed path is non-zero, implying path-dependence for line integrals between points.

Statement A: The electric field generated from Gauss's law is path-independent. Gauss's law is a fundamental law of electrostatics, dealing with electric fields produced by static charge distributions. The electric field in electrostatics is a conservative field. For a conservative field $\vec{E}$, the line integral $\int_A^B \vec{E} \cdot d\vec{l}$ between any two points A and B is independent of the path taken. This property is known as path-independence. Thus, Statement A is correct.

Statement B: The electric field generated due to a changing magnetic flux is also path-independent. According to Faraday's law of electromagnetic induction, a changing magnetic flux induces an electromotive force (EMF), which is associated with an induced electric field. Faraday's law is given by $\oint \vec{E} \cdot d\vec{l} = -\frac{d\Phi_B}{dt}$. The integral on the left side is the circulation of the electric field around a closed loop. If the magnetic flux $\Phi_B$ is changing with time ($\frac{d\Phi_B}{dt} \neq 0$), the line integral of the induced electric field around a closed path is non-zero. This property ($\oint \vec{E} \cdot d\vec{l} \neq 0$) defines a non-conservative field. For a non-conservative field, the line integral between two points is dependent on the path taken. Therefore, the electric field generated due to a changing magnetic flux is path-dependent. Thus, Statement B is incorrect.