Answer to Question #210666 in Electricity and Magnetism for Hey

Question

Maxwell’s equations in integral form are composed of four equations

as follows:

1) Gauss’s law for electrical fields                                ;

2) Faraday’s law of electromagnetic induction                        ;

3) Gauss’s law for magnetic fields                                 ;

4) Ampere’s circuital law                                ;

Answer 1

Part(1)

Gauss law for electric field

$\smallint E.dl=\frac{q}{\epsilon_0}$

Part(2)

Faraday laws for electromagnetic induction

$\smallint E. dl=-\frac{d}{dt}\smallint B.dl$

Part(3)

Gauss law for magnetic field

$\smallint B.da=0$

Part(4)

Ampear circuit law

$$\smallint B.dl= \mu_0(I+\frac{d}{dt}(\epsilon_0\smallint E.dA))$$