Question

Which Maxwell's equation represents Faraday's Law of Induction?

• A. $\nabla \cdot \mathbf{E} = \dfrac{\rho}{\varepsilon_0}$
• B. $\nabla \cdot \mathbf{B} = 0$
• C. $\nabla \times \mathbf{E} = -\dfrac{\partial \mathbf{B}}{\partial t}$
• D. $\nabla \times \mathbf{B} = \mu_0 \mathbf{J} + \mu_0 \varepsilon_0 \dfrac{\partial \mathbf{E}}{\partial t}$

Hint:

Faraday’s Law → Changing magnetic field induces electric field → $\nabla \times E = -\dfrac{\partial B}{\partial t}$.

Answer 1

The Correct Option is C

Concept: Maxwell’s equations describe the behavior of electric and magnetic fields. One of these equations represents Faraday’s Law of Electromagnetic Induction.
Step 1: Understanding Faraday’s Law.
Faraday’s Law states that a changing magnetic field induces an electric field.
Step 2: Mathematical expression.
\[ \nabla \times \mathbf{E} = -\frac{\partial \mathbf{B}}{\partial t} \]
Step 3: Interpretation.

• Time-varying magnetic field produces a circulating electric field
• Basis of transformers, generators, and inductors

Step 4: Eliminating other options.

• (A): Gauss’s Law (electric field)
• (B): Gauss’s Law for magnetism
• (D): Ampere-Maxwell Law

Step 5: Conclusion.
Thus, $\nabla \times \mathbf{E} = -\dfrac{\partial \mathbf{B}}{\partial t}$ represents Faraday’s Law.