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GUJCET · Physics · Moving Charges and Magnetism
An electron and a proton of equal linear momentum enter in the direction perpendicular to uniform magnetic field. If the radii of their circular paths be \(r_e\) and \(r_p\) respectively, then
\(\frac{r_e}{r_p}\) is equal to \(\qquad\) -
(mass of electron \(=m_e\), mass of proton \(=m_p\)
- A \(\left[\frac{m_p}{m_e}\right]^{\frac{1}{2}}\)
- B \(\frac{m_e}{m_p}\)
- C \(\left|\frac{m_e}{m_p}\right|^{\frac{1}{2}}\)
- D 1
Answer & Solution
Correct Answer
(D) 1
Step-by-step Solution
Detailed explanation
D
from \(\frac{m v^2}{r}=q v B\)
\(r=\frac{m U }{q B}=\frac{p}{q B}\)
\(\begin{array}{ll}\therefore r \propto \frac{1}{q} \\ \therefore \frac{r_e}{r_p}=\frac{q_p}{q_e}=\frac{1}{1}=1\end{array}\)
from \(\frac{m v^2}{r}=q v B\)
\(r=\frac{m U }{q B}=\frac{p}{q B}\)
\(\begin{array}{ll}\therefore r \propto \frac{1}{q} \\ \therefore \frac{r_e}{r_p}=\frac{q_p}{q_e}=\frac{1}{1}=1\end{array}\)
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