Question

Ques: Write Maxwell's generalization of ACL. Show that in charging a capacitor, the current produced within the
plates of a capacitor is -​

Answer 1

Answer:

Explanation:

A MOVING CHARGE PRODUCES BOTH ELECTRIC AND MAGNETIC FIELD, AND OSCILATING CHARGE PRODUCES  oscilating magnetic and electric fields.

these oscilating electric and magnetic field with respect to a space and time produce electromagnetic waves.

the propagation of eletromagnetic is shown as:-

Answer 2

Answer:

Explanation:

Question:

To write Maxwell's generalized equation of Ampere's Circuital Law

To show that in charging a capacitor the current produced within the plates of the capacitor is $\sf I= \epsilon_0 \dfrac{d\phi}{dt}$

Answer:

According to Maxwell there arose an inconsistency in Ampere's circuital equation.

To remove this inconsistency, Maxwell suggested the existence of an additional current produced called displacement current and generalized the Ampere's Circuital Law as,

$\sf \oint B.dl=\mu_0\: i_c+\mu_0\: \epsilon_0\: \dfrac{d\phi}{dt}$

$\implies \sf \oint B.dl=\mu_0\:( i_c+ \epsilon_0\: \dfrac{d\phi}{dt})$

where $\sf i_c$ is the conduction current, Φ is the electric flux.

Now finding the current produces within the capacitor,

The flux through the capacitor plates is given as,

$\sf \phi =E.A\: cos\theta$

where

$\sf E=\dfrac{1}{\epsilon_0} \times \dfrac{Q}{A}$

Hence,

$\sf \phi=\dfrac{Q}{\epsilon_0A} \times A$

$\sf \phi=\dfrac{Q}{\epsilon_0}$

Differentiating on both sides with respect to t,

$\sf \dfrac{d\phi}{dt} =\dfrac{d}{dt} \bigg(\dfrac{Q}{\epsilon_0}\bigg)$

$\sf \dfrac{d\phi}{dt} =\dfrac{1}{\epsilon_0} \: \dfrac{dQ}{dt}$

We know that,

$\sf i=\dfrac{dQ}{dt}$

Hence,

$\boxed{\sf i=\epsilon_0\:\dfrac{d\phi}{dt} }$

where Φ is the electric flux.