Question

Extend Ampère's law to account for electrodynamic effects. In other words, find the integral equation analogous to equation (C.7)

c7

Answer 1

We can extend Amperes law to include electrodynamic effect as follows. We start with an example of a capacitor connected to a battery. Since the space between the capacitor plates is empty, the current should not flow in the circuit as the space between acts as an open switch. But we see the current flow in a capacitor circuit. In order to explain this we modify Ampere's law which is given by [B-dī = J. NAS Ĉ CE The electric field between the plates of the capacitor changes as the capacitor starts charging. We construct a Gaussian surface between the plates of the capacitor and from Gauss law we can write q=&ff E- NAS This change in charge produces current between the plates of the capacitor and is given by og He Chi Nas airc We define displacement current as The modified Maxwell ampere law is {B. d = e. ll. 5. Nas + 4.BBC.CË. Nas [B-dī = tem $9.5.Ñas + V.£p.), -ÑAS {B. di dae Juñas + de BJ, . Ñas (B-di de 18 (7+79). Nas This is modified amperes law