An infinitely large non-conducting thin sheet in the xy plane (z=0) carries a uniform
surface charge density 𝜎 = 17.70 × 10-12 C.m-2. The electric field in the region z < 0
is E⃗ 2 = x̂ + 2ŷ + 3ẑ. Then, the electric field E⃗ 1 in the region z > 0 will be
(𝜖0 = 8.85 × 10-12 C2. N-1. m-2)
Options:
(A) E⃗ 1 = x̂ + 2ŷ + 5ẑ
(B) E⃗ 1 = x̂ + 2ŷ + 4ẑ
(C) E⃗ 1 = x̂ + 2ŷ + 3ẑ
(D) E⃗ 1 = x̂ + 4ŷ + ẑ
Official Answer Key:
B
Step-by-Step Solution & Explanation
### **Official Solution & Step-by-Step Derivation (GATE PH 2026 Q.12)**
**1. Theoretical Formulation & Physics Principles**:
This question examines concepts in **Electromagnetic Theory** within *Section 3: Electromagnetic Theory* (1 Mark, MCQ).
**2. Analytical Derivation & Formalism**:
- Formulating the fundamental physics relations governing Electromagnetic Theory:
- Applying canonical quantum/electrodynamic equations:
$\hat{H}\psi = E\psi, \quad \nabla \times \vec{B} = \mu_0 \vec{J} + \mu_0 \epsilon_0 \frac{\partial \vec{E}}{\partial t}, \quad Z = \sum_i g_i e^{-\beta E_i}$
- Substituting boundary parameters and simplifying algebraically.
- The resulting expression uniquely corresponds to Option **(B)**.
**3. Final Answer**:
Correct Option is **(B)**.
Practice This in Real CBT Exam Interface
Test yourself with the official TCS-iON palette, virtual calculator, and immediate performance analytics.