Cyclotrons are used to accelerate ions like deuterons (d) and š¼ particles. Keeping
the magnetic field same for both, d and š¼ are extracted with energies 10 MeV and
20 MeV with extraction radii rd and rš¼, respectively. Taking the masses
Md = 2000 MeV/c2 and Mš¼ = 4000 MeV/c2, t he value of
rš¼
rd
(in integer) is
______
Official Answer Key:
2.5
Step-by-Step Solution & Explanation
### **Official Solution & Step-by-Step Derivation (GATE PH 2025 Q.59)**
**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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