Question

Write any two Maxwell’s equations.

Answer 1

Hint
The set of partial differential equations involving the divergence and curl of electric and magnetic fields are referred to as Maxwell’s equations.

Complete step by step answer
The four Maxwell’s equations that form the basis of classic electromagnetism and depict how electric and magnetic fields are used to generate each other. Maxwell’s first equation represents Gauss's law for electrostatics. According to the law, total electric flux across a closed surface is proportional to the total charge enclosed in the closed surface such that charge is expressed in terms of an integral of charge density. The integral form of Maxwell’s first equation is expressed as,
$\smallint {\rm{\vec E}}.{\rm{d\vec A}} = \dfrac{1}{{{{\rm{\varepsilon }}_0}}}\smallint {\rm{\rho dV}}$
Here, $\dfrac{1}{{{{\rm{\varepsilon }}_0}}}$ is the constant of proportionality. The differential form of this Maxwell’s equation is given by,
$\nabla .{\rm{E}} = \dfrac{{\rm{\rho }}}{{{{\rm{\varepsilon }}_0}}}$
Maxwell’s second equation represents Gauss's law for magnetism. According to the law, the total magnetic flux across a closed surface is zero. This law established the non-existence of magnetic monopoles. The integral form of Maxwell’s second equation is expressed as,
$\smallint {\rm{\vec B}}.{\rm{d\vec A}} = 0$
The differential form of this Maxwell’s equation is given by,
$\nabla .{\rm{B}} = 0$

Note
Maxwell’s equations led to the theory of the existence of light as an electromagnetic wave. Maxwell’s equations do not show much accuracy in the case of extremely strong fields.