Displacement-Current-By-Prof-K-Thyagarajan
1 : Importance in Electromagnetism
Solution :
Recognize the role of displacement current in making Maxwell’s equations consistent and in predicting electromagnetic waves.
2 : Relation with Electric Field
Solution :
Displacement current occurs in regions where there is a time-varying electric field, such as between the plates of a charging capacitor.
3 : Distinction from Conduction Current
Solution :
Know that unlike conduction current, displacement current does not involve physical movement of charge.
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Maxwell’s Amendment to Ampère’s Law: $$[ \nabla \times \mathbf{B} = \mu_0 \mathbf{J} + \mu_0 \varepsilon_0 \frac{\partial \mathbf{E}}{\partial t} ]$$ Understand each term and its implications in different scenarios.
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Displacement Current Density: $$[ \mathbf{J}_d = \varepsilon_0 \frac{\partial \mathbf{E}}{\partial t} ]$$ This is useful in calculating the displacement current in various configurations.
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Displacement Current in a Capacitor: $$[ I_d = \varepsilon_0 A \frac{dE}{dt} ]$$ Here, ( A ) is the area of the capacitor plates, and ( E ) is the electric field between them.
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Electric Field in a Parallel Plate Capacitor: $$[ E = \frac{\sigma}{\varepsilon_0} ]$$ Where σ is the surface charge density on the plates.
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Relation between Electric Flux and Displacement Current: $$[ I_d = \varepsilon_0 \frac{d\Phi_E}{dt} ]$$ Where ΦE is the electric flux.
