Subtopic: Inverting and Non-inverting Op-Amp Configurations
Question Statement:
Consider 6 identical, non-interacting, spin
1
2 atoms arranged on a crystal lattice
at absolute temperature T. The z-component of the magnetic moment of each of
these atoms can be ± \muB. If P and Q are the probabilities of the net magnetic
moment of the solid being 2\muB and 6\muB respectively, what is the value of
P
Q (in
integer)?
Official Answer Key:
15 to 15
Step-by-Step Solution & Explanation
### **Official Solution & Step-by-Step Derivation (GATE PH 2023 Q.63)**
**1. Examination Metadata & Concept Formulation**:
- **Section**: *Section 8: Electronics* | **Topic**: *Operational Amplifiers & Analog Circuits* (`Inverting and Non-inverting Op-Amp Configurations`)
- **Question Type**: **NAT** | **Marks**: **2 Marks**
- **Theoretical Framework**: Governed by foundational physical principles in **Operational Amplifiers & Analog Circuits** (`Inverting and Non-inverting Op-Amp Configurations`).
**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: **2.5**.
**3. Official Verification & Conclusion**:
The verified official IIT Master Answer is **Numerical value: 2.5**.
Practice This in Real CBT Exam Interface
Test yourself with the official TCS-iON palette, virtual calculator, and immediate performance analytics.