Displacement Current Calculation

Question

The electric flux through a certain surface changes at a steady rate of 2.0 × 10⁴ V·m per second, and a student calculates the displacement current.

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Drawing on NCERT Class 12, Chapter 8 (Electromagnetic Waves), the displacement current is defined by I_d = ε₀ (dΦ_E/dt), where ε₀ = 8.85 × 10⁻¹² C²/N·m² and dΦ_E/dt is the rate of change of electric flux through the chosen surface. This quantity arises purely from a time-varying electric field and behaves exactly like a real current in producing a magnetic field, which is why Maxwell could treat conduction and displacement currents on the same footing. The definition also explains why a steady, unchanging field gives zero displacement current: only a changing flux contributes. Substituting the given rate: I_d = 8.85 × 10⁻¹² × 2.0 × 10⁴ = 1.77 × 10⁻⁷ A. The value 8.85 × 10⁻⁸ A wrongly uses half the flux rate or omits the factor of two, giving an incorrect result. The value 2.26 × 10⁶ A is absurd because it divides by ε₀ rather than multiplying, inflating the current enormously. The value 4.43 × 10⁻⁹ A results from a power-of-ten mistake in handling the flux rate. A magnitude check confirms that such a modest flux change produces only a tiny sub-microampere displacement current, consistent with the selected value.

Displacement Current Calculation

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