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GUJCET · Physics · Magnetism And Matter
The ratio of periods of \(\alpha\)-particle and proton moving on circular path in uniform magnetic field is __________.
- A \(2: 1\)
- B \(1: 2\)
- C \(4: 1\)
- D \(1: 4\)
Answer & Solution
Correct Answer
(A) \(2: 1\)
Step-by-step Solution
Detailed explanation
A
\(T =\frac{2 \pi m}{q B}\)
\(\begin{array}{l}\therefore T \alpha \frac{m}{q} \\ \therefore \frac{T_\alpha}{ T _p}=\frac{m_\alpha}{q_\alpha} \times \frac{q_p}{m_p} \\ \therefore \frac{T_\alpha}{ T _p}=\frac{4 m_p}{m_p} \times \frac{q_p}{2 q_p}=2: 1\end{array}\)
\(T =\frac{2 \pi m}{q B}\)
\(\begin{array}{l}\therefore T \alpha \frac{m}{q} \\ \therefore \frac{T_\alpha}{ T _p}=\frac{m_\alpha}{q_\alpha} \times \frac{q_p}{m_p} \\ \therefore \frac{T_\alpha}{ T _p}=\frac{4 m_p}{m_p} \times \frac{q_p}{2 q_p}=2: 1\end{array}\)
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