Question

The equation out of four Maxwell's equations which show electric field lines do not form closed loops

(i) $\oint \overrightarrow{E}·\overrightarrow{ds}=\frac{q_0}{{\in }_0}$

(ii) $\oint \overrightarrow{B}·\overrightarrow{ds}=0$

(iii) $\oint \overrightarrow{E}·\overrightarrow{dt}=\frac{d}{dt}\oint \overrightarrow{B}·\overrightarrow{ds}$

(iv) $\oint \overrightarrow{B}·\overrightarrow{ds}={\mu }_0{\epsilon }_0\frac{d}{dt}\oint \overrightarrow{E}·\overrightarrow{ds}$

• A. (i) Only
• B. (i) and (iv) when E is independent of time.
• C. (iv) only when E is independent of time
• D. None of these.

Answer 1

The correct option is A

(i) Only

1. From gauss theorem$\oint \overrightarrow{E}·\overrightarrow{ds}=\frac{q_0}{{\in }_0}$
2. We know that electric field lines do not form closed loops.
3. This represents the flow of electric field lines to the charge within the enclosed surface.
4. Since $q_o\ne 0$
5. Therefore $\oint \overrightarrow{E}·\overrightarrow{ds}\ne 0$
6. It proves that closed loops are not formed by electric field lines.
7. Whereas all other statements are related to magnetic field lines which form a closed loop.

Hence, option A is the correct answer.