Step 1: Concept Introduction:
Maxwell extended Ampere's circuital law by introducing displacement current. He proposed that a time-varying electric field generates a magnetic field, analogous to conduction current. This effective current from a changing electric field is termed displacement current.
Step 2: Formula:
Displacement current \(I_D\) is defined as:
\[ I_D = \varepsilon_0 \frac{d\Phi_E}{dt} \]
Here, \(\varepsilon_0\) is the permittivity of free space, and \(\Phi_E\) is the electric flux. The term \(\frac{d\Phi_E}{dt}\) signifies the rate of change of electric flux, driven by a fluctuating electric field.
Step 3: Detailed Analysis:
Evaluation of options:
1. Current due to charge flow
Conduction current arises from the movement of charges, such as electrons in a conductor. This is distinct from displacement current and therefore incorrect.
2. Current due to varying gravitational fields
Gravitational fields are unrelated to Maxwell's equations and electromagnetic phenomena. This option is incorrect.
3. Current due to changing electric fields
According to the definition \(I_D = \varepsilon_0 \frac{d\Phi_E}{dt}\), displacement current is generated by a changing electric flux, implying a changing electric field. This is the correct basis. A prime example is the region between the plates of a charging capacitor, where a time-varying electric field produces 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 associated with induced electric fields via Faraday's Law of Induction, not displacement current. This option is incorrect.
Step 4: Conclusion:
Maxwell's displacement current is fundamentally caused by a time-varying electric field.