Displacement Current using Maxwell’s Equation
Maxwell adjusted the main relation of Ampere’s Circuital Law with an additional term. This made the relationship complete and wholesome with both static and time-varying parts present to play their part. Determination of displacement can be done using,
At first, take the magnetic field intensity without the magnetism,
B = μH
Addition of an additional term (Jd) in the above equation,
∇ × H = J + Jd
Performing the divergence action,
∇ . (∇ × H) = 0 = ∇ . J + ∇ . Jd
To define the Jd term,
∇ . Jd = -∇ . J
∇ . Jd = ∂pv / ∂t………….(1)
Using Gauss’s law, ∇ . D = p, Where D is the displacement vector and p is the charge density. Equation (1) becomes,
∂pv / ∂t = (∂ / ∂t) (∇ . D) = ∇ . (∂D / ∂t)
∇ . Jd = ∇ . (∂D / ∂t)
Therefore,
Jd = ∇ . (∂D / ∂t)
This derived term is known as the displacement current density formula. This comes in use when time-varying fields are required. For a constant displacement vector, i.e. a constant charge density the displacement current density vanishes.
So, the integral form of Maxwell’s equation is,
∫E . da = Q / ε0
∫B . da = 0
∫E . dl = -∫δB / δt. (da)
∫B . dl = μ0 l + μ0ε0 ∫(∂E / ∂t)
Displacement Current
Displacement current is the current that is produced by the rate of change of the electric displacement field. It differs from the normal current that is produced by the motion of the electric charge. Displacement current is the quantity explained in Maxwell’s Equation. It is measured in Ampere. Displacement currents are produced by a time-varying electric field rather than moving charges.
In this article we will learn about, displacement current, its characteristics, and others in detail.
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