Answer:
A) A time-varying electric field will produce a magnetic field.
D) A time-varying magnetic field will produce an electric field.
Explanation:
As we know that time varying electric field can induce displacement current in the space
So we will have
[tex]q = A\epsilon_0 E[/tex]
now we have
[tex]i = \frac{dq}{dt}[/tex]
[tex]i = A\epsilon_0\frac{dE}{dt}[/tex]
so it will induce magnetic field given as
[tex]B = \frac{\mu_0 i}{2\pi r}[/tex]
Now similarly time varying magnetic field can induce electric field by Faraday's law given as
[tex]\Delta V = A\frac{dB}{dt}[/tex]
[tex]\int E.dL = \pi r^2\frac{dB}{dt}[/tex]
now we have
[tex]E(2\pi r) = \pi r^2\frac{dB}{dt}[/tex]
so we have
[tex]E = \frac{r}{2}\frac{dB}{dt}[/tex]
so induce electric field is due to magnetic field
