Verified Solution • 2025–26 Session moderate

QPages 230-234: Q31: HC Verma: Concepts of Physics - Volume 2 Magnetic Field Pages 230-234: Q31 Solution: A proton describes a circle of radius 1 cm in a magnetic field…

⚠️ Common Exam Traps & Conceptual Pitfalls

Students often think the radius scales with the charge, not the mass‑to‑charge ratio. Remember the Lorentz force gives $r= rac{m v}{qB}$, so a particle with twice the charge and four times the mass (an $alpha$‑particle) has $r= rac{4m_p v}{2eB}=2,r_p$. Always use $m/q$, not $q/m$, when comparing radii.

A proton describes a circle of radius 1 cm in a magnetic field of strength 0.10 T. What would be the radius of the circle described by an α\alpha-particle moving with the same speed in the same magnetic field?

Step-by-Step Verified Solution

**Answer:** rα=2 cmr_\alpha = 2 \text{ cm}. **Step-by-Step Explanation:** For the proton: rp=mpveB=1 cmr_p = \frac{m_p v}{e B} = 1 \text{ cm}. For the alpha particle: qα=2eq_\alpha = 2e, mα=4mpm_\alpha = 4 m_p. rα=4mpv2eB=2rp=2 cmr_\alpha = \frac{4 m_p v}{2 e B} = 2 r_p = 2 \text{ cm}.

All Questions in this Chapter

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