Question

Maxwell's displacement current is

• A. due to flow of charges
• B. due to changing gravitational field
• C. due to changing electric field
• D. \(\varepsilon_0\) times the rate of change of magnetic flux

Hint:

Remember the symmetry proposed by Maxwell: a changing magnetic field creates an electric field (Faraday's Law), and a changing electric field creates a magnetic field (Displacement Current in Ampere-Maxwell Law).

Answer 1

The Correct Option is C

Step 1: Understanding the Concept:
Maxwell introduced the concept of displacement current to generalize Ampere's circuital law. He postulated that a changing electric field in a region of space produces a magnetic field, just as a conduction current does. This "effective" current arising from a time-varying electric field is called displacement current.

Step 2: Key Formula or Approach:
The displacement current \(I_D\) is defined as: \[ I_D = \varepsilon_0 \frac{d\Phi_E}{dt} \] where \(\varepsilon_0\) is the permittivity of free space and \(\Phi_E\) is the electric flux. The term \(\frac{d\Phi_E}{dt}\) represents the rate of change of electric flux, which is caused by a changing electric field.

Step 3: Detailed Explanation:
Let's analyze the options:
1. due to flow of charges
The current due to the actual flow of charges (like electrons in a wire) is called conduction current. This is not displacement current. So, this is incorrect.
2. due to changing gravitational field
Gravitational fields are not related to electric or magnetic fields in the context of Maxwell's equations. This is incorrect.
3. due to changing electric field
As per the definition \(I_D = \varepsilon_0 \frac{d\Phi_E}{dt}\), a changing electric flux (which implies a changing electric field) is the source of the displacement current. This is the correct definition. A classic example is the space between the plates of a charging capacitor where the electric field changes with time, creating a displacement current.
4. \(\varepsilon_0\) times the rate of change of magnetic flux
The rate of change of magnetic flux, \(\frac{d\Phi_B}{dt}\), is related to the induced electric field (Faraday's Law of Induction), not the displacement current. This is incorrect.

Step 4: Final Answer:
Maxwell's displacement current is fundamentally due to a time-varying electric field.