Question

Which of the following is the right derivation for Ampere-Maxwell law?

• A. $\oint \overrightarrow{B}.\overrightarrow{dl}={\mu }_0{i}_c+4\pi {\mu }_0{\epsilon }_0\frac{d{\varphi }_E}{dt}$
• B. $\oint \overrightarrow{B}.\overrightarrow{dl}={\mu }_0{i}_c+3{\mu }_0{\epsilon }_0\frac{d{\varphi }_E}{idt}$
• C. $\oint \overrightarrow{B}.\overrightarrow{dl}={\mu }_0{i}_c+{\mu }_0{\epsilon }_0\frac{d{\varphi }_E}{dt}$
• D. $\oint \overrightarrow{B}.\overrightarrow{dl}={\mu }_0{i}_c+\frac{{\mu }_0}{{\epsilon }_0}\frac{d{\varphi }_E}{dt}$

Answer 1

Answer: (C)

$\oint \overrightarrow{B}.\overrightarrow{dl}={\mu }_0{i}_c+{\mu }_0{\epsilon }_0\frac{d{\varphi }_E}{dt}$

Maxwell pointed out the inconsistency of the Ampere's circuital law. He said that there is also a current flow, in the space between the plates of a capacitor due to time varying electric field between the plates. Maxwell named this current as displacement current ($i_d$). This concept makes a continuous flow of current in an electric circuit containing a capacitor.

Now the improved Ampere's law, called Ampere-Maxwell's law is given by:

$\oint \overrightarrow{B}.\overrightarrow{d}l={\mu }_0{i}_c+{\mu }_0{\epsilon }_0\frac{d{\varphi }_E}{dt}$