Consider an infinitely long solenoid with N turns per unit length, radius R and carrying a
current I(t) = 𝛼 cos 𝜔t, where 𝛼 is a constant and 𝜔 is the angular frequency. The
magnitude of electric field at the surface of the solenoid is
(A)
1
2 𝜇0NR𝜔𝛼 sin 𝜔t (B)
1
2 𝜇0𝜔NR cos 𝜔t
(C) 𝜇0NR𝜔𝛼 sin 𝜔t (D) 𝜇0𝜔NR cos 𝜔t
Official Answer Key:
2.5
Step-by-Step Solution & Explanation
### **Official Solution & Step-by-Step Derivation (GATE PH 2018 Q.29)**
**1. Theoretical Formulation & Physics Principles**:
This question examines concepts in **Electromagnetic Theory** within *Section 3: Electromagnetic Theory* (1 Mark, 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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