Question:
Two charged particles $2q$ and $q$ having equal momentum enter a uniform magnetic field in a direction perpendicular to the magnetic field. Then their respective radii of circular paths $r_1$ and $r_2$ are in the ratio
Two charged particles $2q$ and $q$ having equal momentum enter a uniform magnetic field in a direction perpendicular to the magnetic field. Then their respective radii of circular paths $r_1$ and $r_2$ are in the ratio
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For same momentum, radius is inversely proportional to charge.
Updated On: Apr 24, 2026
- $2:1$
- $1:4$
- $1:2$
- $1:3$
- $4:1$
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The Correct Option is C
Solution and Explanation
Concept:
• Radius in magnetic field: \[ r = \frac{p}{qB} \]
Step 1: Given
Momentum same $\Rightarrow p = constant$
Step 2: Relation
\[ r \propto \frac{1}{q} \]
Step 3: Ratio
\[ r_1 : r_2 = \frac{1}{2q} : \frac{1}{q} = 1 : 2 \] Final Conclusion:
Option (C)
• Radius in magnetic field: \[ r = \frac{p}{qB} \]
Step 1: Given
Momentum same $\Rightarrow p = constant$
Step 2: Relation
\[ r \propto \frac{1}{q} \]
Step 3: Ratio
\[ r_1 : r_2 = \frac{1}{2q} : \frac{1}{q} = 1 : 2 \] Final Conclusion:
Option (C)
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