A ray of light inside Region 1 in the xy- plane is incident at the semicircular boundary that carries
no free charges. The electric field at the point ( )0 , /4P r π in plane polar coordinates is
1 73ˆˆrE ee ϕ= -
, where ˆˆ andree ϕ are the unit vectors. The em erging ray in R egion 2 has the
electric field 2E
parallel to x- axis. If 12 and εε are the dielectric constants of Region 1 and
Region 2 respectively, then 2
1
ε
ε
is ____________________________
PH 7/10
PH (GATE 2014)
1 PHYSICS-PH
Official Answer Key:
2.5
Step-by-Step Solution & Explanation
### **Official Solution & Step-by-Step Derivation (GATE PH 2014 Q.36)**
**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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