91Ó°ÊÓ

The quantities of electrostatics.

The source charge distribution is$\mathrm{ÒÏ}$.

The field is$E$.

The scaler potential is $V$.

The quantities of magnetostatics

The current density is$J$.

The vector potential is$A$.

The field is$B$.

$r$The expression for the current density is given by,

localid="1658117699866" $J=\frac{1}{{\mathrm{μ}}_0}(∇×B)$

Herelocalid="1658117712093" ${\mathrm{μ}}_0$is the permeability of the free space.

The current density can also be expressed as,

localid="1658118201653" $J=−{\mathrm{Î\mu }}_0\frac{∂E}{∂t}$

Here localid="1658117721372" ${\mathrm{Î\mu }}_0$is the permeability of free space.

The electric field strength is given by,

localid="1658117726324" $E=\frac{1}{4\mathrm{Ï€}{\mathrm{Î\mu }}_0}∫\frac{\mathrm{ÒÏ}}{r^2}\widehat{r}dr$

Here,$\widehat{r}$is the unit vector of the position vectorlocalid="1658117731358" $r$.

Form the Poisson’s equation is given by,

localid="1658118216349" $∇{}^{2}v=\frac{p}{{\mathrm{Î\mu }}_0}$

The expression for the scaler potential is given by,

localid="1658117736537" $V=\frac{1}{4\mathrm{Ï€}{\mathrm{Î\mu }}_0}∫\frac{\mathrm{ÒÏ}}{r}dr$

The relationship between electric field and scaler potential is given by,

localid="1658117743380" $E=−∇V$

The scalar potential in term of line integral of electrical field is given by.

localid="1658117758220" $V=−∫Edl$

From the maxwell’s equation of electromagnetism is given by,

localid="1658117764321" $∇â‹\dots B=−\frac{1}{c^2}\frac{∂V}{∂t}$

The electric field in terms of vector potentiallocalid="1658407444461" $A$is given by,

localid="1658117772742" $E=∇V−\frac{∂A}{∂t}$

Therefore, triangle diagram for electrodynamics analogous to triangle diagram of electrostatics withsource localid="1658407429337" $J$, localid="1658407433898" $\mathrm{ÒÏ}$and field localid="1658407449348" $E$andlocalid="1658407454000" $B$, potentiallocalid="1658407459615" $V$andlocalid="1658407464380" $A$is shown below.