# Displacement Current

## Displacement Current

In electromagnetism, the displacement current is a quantity appearing in Maxwell’s equations that is defined in terms of the rate of change of electric displacement field. Displacement current has the units of electric current density and it has an associated magnetic field. However, it is not an electric current of moving charges, but a time varying electric field.

What is Displacement Current?

Displacement current is a quantity appearing in Maxwell’s equations. Displacement current definition is defined in terms of the rate of change of the electric displacement field. Physical behavior of displacement current is same as that of induction current.

Displacement Current Formula:

Consider a simple circuit containing a battery, a parallel plate capacitor and a switch. Immediately after switch is closed a current flows through the conducting section of the circuit, resulting in an accumulation of positive charge on one plate of the capacitor and equal accumulation of negative charge on other plate.

For a given charge density σ on the capacitor plates, the electric field in the dielectric gap is:

Electric Field (E) = σ/ ε; Where, ε = Permittivity of the dielectric.

Now,

σ = ε E = D; Where, D = Electric Displacement.

During the charging of the capacitor, the charge density on the plates is changing at a rate of $$\frac{d\sigma }{dt}$$ and the value of the displacement in the dielectric gap changes accordingly.

$$\frac{d\sigma }{dt}=\frac{dD}{dt}$$.

$$\frac{d\sigma }{dt}={{\varepsilon }_{0}}\frac{dE}{dt}+\frac{dP}{dt}.$$.

Here, $$\frac{dP}{dt}$$ is the rate of change of polarization. This is associated with the actual motion of charge in the dielectric, corresponding as it does to the rotation of permanent dipoles and $${{\varepsilon }_{0}}\frac{dE}{dt}$$ is the current that is associated with a change in the electric field strength, even when there is a vacuum between the capacitor plates.