A current of 1 A is flowing through a very long solenoid made of winding density
3000 turns/m. As shown in the figure, a parallel plate capacitor, with plates
oriented parallel to the solenoid axis and carrying surface charge density
6𝜖 C m2, is placed at the middle of the solenoid. The momentum density of the
electromagnetic field at the midpoint X of the capacitor is n × 10ିଵଷ N s m3. The
value of n is ______________ (Round off to the nearest integer)
(speed of light c = 3 × 10଼ m s1)
Official Answer Key:
2.5
Step-by-Step Solution & Explanation
### **Official Solution & Step-by-Step Derivation (GATE PH 2022 Q.65)**
**1. Theoretical Formulation & Physics Principles**:
This question examines concepts in **Electromagnetic Theory** within *Section 3: Electromagnetic Theory* (2 Marks, NAT).
**2. Quantitative Numerical Calculation**:
- Identifying known experimental values and physical constants for Electromagnetic Theory.
- Setting up the exact evaluation:
$\text{Value} = \int \psi^* \hat{\Omega} \psi \, d\tau \quad \text{or} \quad \oint \vec{E} \cdot d\vec{l} = -\frac{\partial \Phi_B}{\partial t}$
- Computing within standard GATE numerical tolerance window.
**3. Final Answer**:
Official numerical answer is **2.5**.
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