The additional term that was added to Ampere’s law under time variation represents current that is not due to free electrons (charge) flowing directly through a cross-sectional surface. This current is called: A. None of these B. Free-electron current C. Displacement current D. Conduction current E. Convection current
The correct answer and explanation is:
Correct Answer: C. Displacement current
Explanation (300 words):
In classical electromagnetism, Ampère’s Law originally described the magnetic field generated by steady (unchanging) currents. However, James Clerk Maxwell recognized a critical limitation in the original form of this law. When applied to time-varying electric fields, such as those in a charging capacitor, Ampère’s Law alone led to inconsistencies with the principle of charge conservation (continuity equation).
To resolve this, Maxwell added an extra term to Ampère’s Law, introducing what is known as the displacement current. This term accounts for the changing electric field in regions where there is no actual movement of free charge (like between the plates of a capacitor).
The modified form of Ampère’s Law (one of Maxwell’s equations) is: ∇⃗×B⃗=μ0J⃗+μ0ε0∂E⃗∂t\vec{\nabla} \times \vec{B} = \mu_0 \vec{J} + \mu_0\varepsilon_0 \frac{\partial \vec{E}}{\partial t}
Where:
- B⃗\vec{B} is the magnetic field,
- J⃗\vec{J} is the conduction current density (due to actual moving charges),
- ε0∂E⃗∂t\varepsilon_0 \frac{\partial \vec{E}}{\partial t} is the displacement current density,
- μ0\mu_0 is the permeability of free space,
- ε0\varepsilon_0 is the permittivity of free space.
The displacement current is not a “real” current in the sense of flowing electrons; instead, it’s a mathematical term that represents the effect of a time-varying electric field. It allows the continuity of the magnetic field in places where there is no physical current, such as the space between capacitor plates during charging.
Summary:
- Displacement current is the correct answer.
- It is essential for the consistency of Maxwell’s equations.
- It enables electromagnetic waves to propagate in a vacuum, as in light.
Thus, option C: Displacement current is the correct and most complete answer.