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Displacement Current and Maxwell's Correction

Displacement current is the effective current associated with a time-varying electric flux. It is given by Id = ε0 dPhiE/dt and is introduced in Ampere's law to account for changing electric fields.

In one line: Changing electric flux plays the role of current for magnetic field production.

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Understand it

  • In a charging capacitor, conduction current flows in the wires but no charge crosses the insulating gap between the plates.
  • However, the electric field between the plates changes with time, so the electric flux changes.
  • Maxwell showed that this changing electric flux acts like a current for producing magnetic field.
  • The corrected law treats conduction current and displacement current together, making the magnetic field description continuous across the circuit.

Example

During charging of a parallel-plate capacitor, the current in the connecting wire is conduction current, while the current between the plates is displacement current due to the changing electric field.

Formula and rule

Formula: Id = ε0 dPhiE/dt.

Here Id is displacement current in ampere, ε0 is permittivity of free space in F m−1, PhiE is electric flux in N m2 C−1 or V m, and t is time in second.

Corrected Ampere-Maxwell law: integral B dot dl = μ0(I + Id).

Use it when electric flux changes with time, especially in capacitors or time-varying fields.

See it worked out

Follow the example line by line, then use the same method on new questions.

Worked example

For a charging capacitor, suppose electric flux between plates changes at 5.0 × 1012 V m s−1.

  1. 1Id = ε0 dPhiE/dt = 8.85 × 10−12 × 5.0 × 1012 = 44.25 A.
  2. 2Interpretation: the changing electric field has the same magnetic effect as a current of about 44 A in the gap.

Method you can reuse

  1. 1Identify whether electric flux is changing with time.
  2. 2Write Id = ε0 dPhiE/dt.
  3. 3Substitute flux-rate values with SI units.
  4. 4For law-based answers, write integral B dot dl = μ0(I + Id).
  5. 5Explain that changing electric field produces magnetic field even without conduction across the gap.

Visual tip

A useful diagram shows a capacitor being charged: battery, connecting wires, plates, conduction current in the wire, electric field between plates, and displacement current shown in the gap. The key point is that current continuity is maintained without charges crossing the dielectric.

Check yourself

Answer the question in your head before opening the answer.

Try it yourself

Why is displacement current introduced while studying a charging capacitor?

Think first, then show answer
Displacement current is introduced because no conduction current crosses the gap between the capacitor plates, yet the changing electric field there produces a magnetic field. Maxwell represented this effect as Id = ε0 dPhiE/dt so that the same current effect is accounted for throughout the circuit.

Common wrong answer

Displacement current is the current of electrons moving through the dielectric.

Why it loses marks: The correction is that it is not conduction through the dielectric; it is due to changing electric flux.

Don't mix this up

Students often think displacement current means actual flow of charges through the dielectric between capacitor plates. It does not require charge transport through the gap; it is linked to changing electric flux.

Exam tip

In answers, clearly distinguish conduction current I from displacement current Id and mention that Maxwell's correction makes Ampere's law valid for time-varying electric fields.

Write it in the exam

Each point is worth about one mark. Write point 1 for a 1-mark question and keep adding points as the marks go up.

How CBSE asks it

Common questions ask for the need of displacement current, the expression for Id, or the resolution of the capacitor paradox in Ampere's law. Assertion-reason items often test whether displacement current exists where electric flux changes.
  1. 1

    Enough for 1 mark

    Displacement current is the effective current associated with a time-varying electric flux. It is given by Id = ε0 dPhiE/dt and is introduced in Ampere's law to account for changing electric fields.

  2. 2

    Add for 2 marks

    Example: During charging of a parallel-plate capacitor, the current in the connecting wire is conduction current, while the current between the plates is displacement current due to the changing electric field.

  3. 3

    Add for 3 marks

    In a charging capacitor, conduction current flows in the wires but no charge crosses the insulating gap between the plates.

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