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AIIMS 2004
Exam
AIIMS
Year
2004
Subject
Physics
Chapter
Magnetic Effects of Current

AIIMS 2004 · Physics · Magnetic Effects of Current

A proton and an α -particle, moving with the same velocity, enter...

A proton and an α\alpha-particle, moving with the same velocity, enter into a uniform magnetic field, acting normal to the plane of their motion. The ratio of the radii of the circular paths described by the proton and α\alpha-particle is

Options

  1. A1:21: 2
  2. B1:41: 4
  3. C1:161: 16
  4. D4:14: 1.

Correct answer

A. 1:21: 2

Step-by-step solution

While describing circular path, the centripetal and centrifugal forces are balancing each other. \Rightarrow \quad mv2r=\frac{m v^2}{r}=q v B (as the uniform magnetic field is acting normal to the plane)⇒r=mvqB⇒rprα=mpveB×2eBmαv=2mp4mp[ as mα=4mp]∴rp:rα=1:2\begin{aligned}& \Rightarrow \quad r=\frac{m v}{q B} \Rightarrow \frac{r_p}{r_\alpha}=\frac{m_p v}{e B} \times \frac{2 e B}{m_\alpha v}=\frac{2 m_p}{4 m_p}\left[\text{ as }m_\alpha=4 m_p\right] \\ & \therefore \quad r_p: r_\alpha=1: 2 \end{aligned}
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