An accelerated electric charge emits

Show that the magnetic field $B$ at a point in between the plates of a parallel-plate capacitor during charging is $B = \frac{{\mu _0 \epsilon _0 r}}{2} \cdot \frac{{dE}}{{dt}}$ (symbols have their usual meanings).

What is the phase difference between the space current and the capacitive displacement current produced when radio waves pass through the ionosphere?

Match List-$I$ with List-$II$ and choose the correct answer from the options given below:
| List-$I$ | List-$II$ |
| :--- | :--- |
| $A$. Gauss's law of magnetostatics | $I$. $\oint \vec{E} \cdot d\vec{a} = \frac{1}{\epsilon_0} \int \rho dV$ |
| $B$. Faraday's law of electromagnetic induction | $II$. $\oint \vec{B} \cdot d\vec{a} = 0$ |
| $C$. Ampere's law | $III$. $\oint \vec{E} \cdot d\vec{l} = -\frac{d}{dt} \int \vec{B} \cdot d\vec{a}$ |
| $D$. Gauss's law of electrostatics | $IV$. $\oint \vec{B} \cdot d\vec{l} = \mu_0 I$ |

What was used to detect the radio waves?

Which of the following Maxwell's equations is valid for time-varying conditions but not valid for static conditions?