An infinitely large thin sheet in the xy-plane carries uniform positive charge density and
is moving with constant velocity v in the +x direction (see figure below). The direction
of the corresponding Poynting vector is
Options:
(A) +x for both z < 0 and z > 0
(B) +x for z < 0 and -x for z > 0
(C) -x for z < 0 and +x for z > 0
(D) -x for both z < 0 and z > 0
Official Answer Key:
A
Step-by-Step Solution & Explanation
### **Official Solution & Step-by-Step Derivation (GATE PH 2026 Q.47)**
**1. Examination Metadata & Concept Formulation**:
- **Section**: *Section 3: Electromagnetic Theory* | **Topic**: *Maxwell's Equations & Conservation Laws* (`Poynting Vector & Electromagnetic Energy Conservation`)
- **Question Type**: **MCQ** | **Marks**: **2 Marks**
- **Theoretical Framework**: Governed by foundational physical principles in **Maxwell's Equations & Conservation Laws** (`Poynting Vector & Electromagnetic Energy Conservation`).
**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): `+x for z < 0 and -x for z > 0`**.
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