KCET · Physics · Magnetic Effects of Current
A proton and an alpha-particle moving with the same velocity enter a uniform magnetic field with their velocities perpendicular to the magnetic field. The ratio of radii of their circular paths is
- A \(2: 1\)
- B \(1: 4\)
- C \(4: 1\)
- D \(1: 2\)
Answer & Solution
Correct Answer
(D) \(1: 2\)
Step-by-step Solution
Detailed explanation
Radius of charged particle moving on circular
path in uniform magnetic field,
\(r =\frac{m v}{B q} \)
\( r \propto \frac{m}{q} \)
\( \frac{r_p}{r_\alpha} =\frac{m_p}{m_\alpha} \cdot \frac{q_\alpha}{q_p}=\frac{m_p}{4 m_p} \times \frac{2 e}{e}=\frac{1}{2}\)
\(\Rightarrow r_p: r_\alpha=1: 2\)
path in uniform magnetic field,
\(r =\frac{m v}{B q} \)
\( r \propto \frac{m}{q} \)
\( \frac{r_p}{r_\alpha} =\frac{m_p}{m_\alpha} \cdot \frac{q_\alpha}{q_p}=\frac{m_p}{4 m_p} \times \frac{2 e}{e}=\frac{1}{2}\)
\(\Rightarrow r_p: r_\alpha=1: 2\)
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