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

Step 1: Understanding the Concept:
Faraday's Law of Induction states that a time-varying magnetic field induces an electromotive force (EMF), which creates an electric field.
Step 2: Detailed Explanation:
Maxwell's differential form of this law relates the curl of the electric field ($\mathbf{E}$) to the rate of change of the magnetic field ($\mathbf{B}$).
\[ \nabla \times \mathbf{E} = -\frac{\partial \mathbf{B}}{\partial t} \]
- (A) is Gauss's Law for electric fields.
- (B) is Gauss's Law for magnetism (no monopoles).
- (D) is the Ampere-Maxwell Law.
Step 3: Final Answer:
The equation $\nabla \times \mathbf{E} = -\frac{\partial \mathbf{B}}{\partial t}$ represents Faraday's Law.