Question

Which one of the following laws is modified by Maxwell to obtain four electromagnetic equations known as Maxwell's equations?

• A. Gauss's law of electricity
• B. Gauss's law of magnetism
• C. Faraday's law
• D. Ampere's circuit law

Hint:

The four Maxwell's equations are:
1. Gauss's Law of Electrostatics
2. Gauss's Law of Magnetism
3. Faraday's Law of Induction
4. Ampere-Maxwell Law (the only one modified by Maxwell).

Answer 1

The Correct Option is D

Step 1: Check charge continuity across a charging capacitor.
Between the plates of a charging capacitor, no conduction current flows, yet charge is clearly building up on the plates, so a term is missing from the equation used at that time.
Step 2: Trace this back to Gauss's law.
Since $Q = \varepsilon_0\oint \vec{E}\cdot d\vec{A}$, differentiating gives $\dfrac{dQ}{dt} = \varepsilon_0\dfrac{d\Phi_E}{dt}$, meaning a changing electric flux behaves exactly like a current for continuity purposes.
Step 3: Identify which law this term gets added to.
Maxwell added this displacement current term $\varepsilon_0\dfrac{d\Phi_E}{dt}$ into Ampere's original equation, making it consistent for all surfaces, charging capacitor included. \[ \boxed{\text{Ampere's circuital law}} \]