Consider a particle of mass m = 9.0 × 10-5 kg and charge q = 3.0 × 10-4 C in a
uniform electromagnetic field E⃗ = 2 x̂ V. m-1, B⃗ = 3 ẑ V. m-2. s. The particle is
released from the coordinates (0, 5 m , 0) at time t = 0. Starting from initial speed zero, it
comes back to the y-axis for the first time at time t. The value of t in seconds (rounded
off to two decimal places) is _____
Official Answer Key:
2.5
Step-by-Step Solution & Explanation
### **Official Solution & Step-by-Step Derivation (GATE PH 2026 Q.57)**
**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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