91Ó°ÊÓ

Each of Maxwell's four equations represents a certain aspect of the interaction between electric and magnetic fields. They are as follows: (i) Gauss's law for electricity: \(\oint \vec{E} \cdot \overrightarrow{d s}=\frac{q_{0}}{\varepsilon_{0}}\) - This equation relates the electric field, E, to its source, the charge q. (ii) Gauss's law for magnetism: \(\oint \vec{B} \cdot \overrightarrow{d s}=0\) - This equation states that there are no isolated magnetic charges or "magnetic monopoles". The net magnetic flux through any closed surface is zero. (iii) Faraday's law of electromagnetic induction: \(\oint \vec{E} \cdot \overrightarrow{d l}=-\frac{d}{d t} \oint \vec{B} \cdot \overrightarrow{d s}\) - This equation relates the time-varying magnetic field, B, to the induced electric field, E. (iv) Ampere-Maxwell law: \(\oint \vec{B} \cdot \overrightarrow{d l}=\mu_{0} \varepsilon_{0} \frac{d}{d t} \oint \vec{E} \cdot \overrightarrow{d s}+ \mu_0 I_{enc}\) - This equation relates the time-varying electric field, E, or total electric current to the magnetic field, B.

From the explanation of each equation, we can identify the equations that have sources of electric field, E and magnetic field, B: (i) Gauss's law for electricity has a source of E field, which is the total electric charge enclosed by the surface. (iv) Ampere-Maxwell law has a source of B field, which is the total electric current enclosed by the loop and the time-varying electric field. Based on these observations, the correct answer is (D), as the equations (i) and (iv) have sources of E and B fields respectively.