# Is the electrical signal delivered to a load by a receiving antenna always $\propto \frac {\partial}{\partial t}$ of the $\vec{E}$ or $\vec{B}$ field?

A time-varying $B(t)$ field through a loop antenna induces a voltage proportional to $\dot{B}(t)$. A Hertzian dipole along a time-varying $E(t)$ field also induces a voltage across a load--while I haven't seen a rigorous derivation of what it is, since we have a zero output when $\dot{E}(t) = 0$, it seems likely to me that the output is proportional to $\dot{E}(t)$.

So I was wondering if this is true of any antenna? Since in radiation, at any point in the far field, the magnitudes $E(t) = cB(t)$, is it true the voltage across any resistive load at the receiver is proportional to $\dot{E}(t)$?

If so, since in the far field $E(t) \propto \dot{I}(t_r)$, does this mean that the voltage across the load in the receiver is proportional to $\ddot{I}(t_r)$? And since this would mean that the power transferred to the load would depend on $\ddot{I}(t_r)$ as well, and we know that the Poynting vector depends on $\dot{I}(t_r)$, what happens to the difference?

• The answer to your question depends on whether you want a theoretical or experimental response. In the latter case, the definition of the "size" of $\Delta t$ for any measurement depends upon the electronics. In the former case, one could imagine a static E or B that could affect currents in a conductor. The effects of such fields could presumably be measured. Apr 26 '15 at 12:29