Question

Which of the following are correct form of Maxwell's equation?
A. \(\vec{\nabla}\cdot\vec{B}=0\),
B. \(\vec{\nabla}\cdot\vec{E}=\dfrac{\rho}{\epsilon_0}\),
C. \(\vec{\nabla}\times\vec{E}=-\dfrac{\partial \vec{B}}{\partial t}\),
D. \(\dfrac{1}{2}\left(\epsilon_0E^2+\dfrac{B^2}{\mu_0}\right)=U\). Choose the correct answer from the options given below:

• A. A, B, C Only
• B. A, C, D Only
• C. A, B, D Only
• D. A, D Only

Hint:

Maxwell's equations include Gauss law, Gauss law for magnetism, Faraday law and Ampere-Maxwell law.

Answer 1

The Correct Option is A

Concept:
Maxwell's equations describe electric and magnetic fields and their relation with charge and current.

Step 1: Check statement A.
Gauss law for magnetism is: \[ \vec{\nabla}\cdot\vec{B}=0 \] This means magnetic monopoles do not exist. \[ A \text{ is correct} \]

Step 2: Check statement B.
Gauss law for electricity is: \[ \vec{\nabla}\cdot\vec{E}=\frac{\rho}{\epsilon_0} \] \[ B \text{ is correct} \]

Step 3: Check statement C.
Faraday's law of electromagnetic induction is: \[ \vec{\nabla}\times\vec{E}=-\frac{\partial \vec{B}}{\partial t} \] \[ C \text{ is correct} \]

Step 4: Check statement D.
The expression: \[ U=\frac{1}{2}\left(\epsilon_0E^2+\frac{B^2}{\mu_0}\right) \] is electromagnetic energy density, not Maxwell's equation. \[ D \text{ is incorrect} \] Thus, correct Maxwell equations are: \[ A,B,C \] \[ \therefore \text{Correct Answer is (A)} \]