Question

Match the following Maxwell's equations: (The symbols used here have their usual meanings)

• A. a - i, b - iii, c - iv, d - ii
• B. a - ii, b - iii, c - i, d - iv
• C. a - i, b - ii, c - iii, d - iv
• D. a - ii, b - iii, c - iv, d - i

Hint:

To remember them:
1. Gauss Electro: \( \Phi_E \propto Q \).
2. Gauss Magnet: \( \Phi_B = 0 \).
3. Faraday: \( \text{emf} = -d\Phi_B/dt \).
4. Ampere-Maxwell: \( B \) loop relates to \( I \) and \( d\Phi_E/dt \).

Answer 1

The Correct Option is A

Step 1: Understanding the Question:
The task is to match the names of the four fundamental equations of electromagnetism with their integral mathematical forms as formulated by Maxwell.
Step 3: Detailed Explanation:
- (a) Gauss' law for electrostatics: States that the net electric flux through any closed surface is proportional to the enclosed electric charge. The formula is \( \oint \vec{E} \cdot d\vec{A} = \frac{Q}{\epsilon_0} \). This matches with (i).
- (b) Gauss' law for magnetism: States that the net magnetic flux through any closed surface is always zero, implying that magnetic monopoles do not exist. The formula is \( \oint \vec{B} \cdot d\vec{A} = 0 \). This matches with (iii).
- (c) Faraday's law: States that a changing magnetic field induces an electromotive force (emf), where the line integral of the electric field around a closed loop is equal to the negative rate of change of magnetic flux. The formula is \( \oint \vec{E} \cdot d\vec{l} = -\frac{d\phi_B}{dt} \). This matches with (iv).
- (d) Ampere-Maxwell's law: Generalizes Ampere's law by including displacement current. It states that magnetic fields are produced by both conduction currents (\( i_c \)) and time-varying electric fields (flux \( \phi_E \)). The formula is \( \oint \vec{B} \cdot d\vec{l} = \mu_0 [i_c + \epsilon_0 \frac{d\phi_E}{dt}] \). This matches with (ii).
Mapping: a \(\rightarrow\) i, b \(\rightarrow\) iii, c \(\rightarrow\) iv, d \(\rightarrow\) ii.
Step 4: Final Answer:
The correct matching sequence is given in code (1).