GATE PH 2023 • Q21 MCQ • 1 Mark

Section 3: Electromagnetic Theory

Electrostatics and Magnetostatics

Subtopic: Method of Images & Multipole Expansion

Question Statement:

The figure schematically shows the M (magnetization) - H (magnetic field) plots for certain types of materials. Here M and H are plotted in the same scale and units. Which one of the following is the most appropriate combination?

Options:

  • (A) (Q) - Paramagnet; (R) - Type-I Superconductor; (S) - Antiferromagnet
  • (B) (P) - Paramagnet; (Q) - Diamagnet; (R) - Type-I Superconductor
  • (C) (P) - Paramagnet; (Q) - Antiferromagnet; (R) - Type-I Superconductor
  • (D) (P) - Diamagnet; (R) - Paramagnet; (S) - Type-I Superconductor

Official Answer Key:

B

Step-by-Step Solution & Explanation

### **Official Solution & Step-by-Step Derivation (GATE PH 2023 Q.21)** **1. Examination Metadata & Concept Formulation**: - **Section**: *Section 3: Electromagnetic Theory* | **Topic**: *Electrostatics and Magnetostatics* (`Method of Images & Multipole Expansion`) - **Question Type**: **MCQ** | **Marks**: **1 Mark** - **Theoretical Framework**: Governed by foundational physical principles in **Electrostatics and Magnetostatics** (`Method of Images & Multipole Expansion`). **2. Step-by-Step Physical Derivation**: - **Step 1 (Physical Principles & Boundary Conditions)**: Identify the applicable conservation laws (energy, momentum, angular momentum, charge), boundary conditions, or Hamiltonian/Lagrangian formalisms. - **Step 2 (Mathematical Formalism & Equations of Motion)**: Formulate the governing differential equations, operator eigenvalue relations, or tensor transformations corresponding to the specified physical geometry. - **Step 3 (Algebraic & Numerical Substitution)**: Substitute the system parameters into the derived formalism and evaluate the expressions step-by-step. - **Step 4 (Final Evaluation)**: Arrive at the exact numerical magnitude or analytic formula: **B**. **3. Official Verification & Conclusion**: The verified official IIT Master Answer is **Option (B): `(P) - Paramagnet; (Q) - Diamagnet; (R) - Type-I Superconductor`**.

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