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GUJCET · Physics · Moving Charges and Magnetism
The ratio of time 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
\(\begin{aligned} T =\frac{2 \pi m}{q B} \\ T \propto \frac{m}{q} \\ \frac{T_\alpha}{ T _p} =\frac{m_\alpha}{q_\alpha} \times \frac{q_p}{m_p} \\ \frac{T_\alpha}{ T _p} =\frac{4 m_p}{2 q_p} \times \frac{q_p}{m_p}\end{aligned}\)
\(\therefore \frac{ T _\alpha}{ T _p}=\frac{2}{1}\)
\(\begin{aligned} T =\frac{2 \pi m}{q B} \\ T \propto \frac{m}{q} \\ \frac{T_\alpha}{ T _p} =\frac{m_\alpha}{q_\alpha} \times \frac{q_p}{m_p} \\ \frac{T_\alpha}{ T _p} =\frac{4 m_p}{2 q_p} \times \frac{q_p}{m_p}\end{aligned}\)
\(\therefore \frac{ T _\alpha}{ T _p}=\frac{2}{1}\)
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