Shortcut Methods and Tricks for Numerical on Displacement Current

JEE Main Level

• Displacement current density (Jd):

  • Remember the formula: Jd = ϵ0 * (∂E/∂t), where ϵ0 is the permittivity of free space (8.85 × 10^−12 C^2 N−1 m−2) and (∂E/∂t) represents the rate of change of the electric field with respect to time.

• Magnitude of displacement current (Id):

  • Use the formula: Id = Jd * A, where A is the area perpendicular to the direction of the displacement current.

• Displacement current through a parallel-plate capacitor:

  • Apply the formula: Id = ϵ0 * (A/d) * (dV/dt), where d is the distance between the plates, A is the area of the plates, and (dV/dt) is the rate of change of potential difference across the capacitor.

• Displacement current in a sinusoidal AC circuit:

  • For a sinusoidal AC circuit with angular frequency ω and amplitude of electric field E0, use the formula: Id = ϵ0 * ω * E0 * A.

CBSE Board Level

• Relation between displacement current and rate of change of electric field:

  • Remember the proportionality: Jd ∝ (∂E/∂t).

• Relation between displacement current and conduction current:

  • Use the equation: Jd = -J.

• Significance of displacement current in AC circuits:

  • Understand that the displacement current becomes significant at high frequencies, affecting the behavior of AC circuits.

• Role of displacement current in electrical devices:

  • Recognize the importance of displacement current in the proper functioning of transformers and capacitors.

• Generation of electromagnetic waves:

  • Remember that the displacement current is crucial for generating electromagnetic waves, including light and radio waves.