Question

A charged particle is moving in a uniform magnetic field in a circular path of radius \( R \). When the energy of the particle becomes three times the original, the new radius will be

• A. \( \frac{R}{3} \)
• B. \( R \)
• C. \( 3R \)
• D. \( \sqrt{3} R \)

Hint:

Remember, when the energy of a particle increases, the velocity and radius increase by the square root of the energy factor.

Answer 1

The Correct Option is C

Step 1: Energy and radius relationship.
The kinetic energy of the charged particle in a magnetic field is given by: \[ E = \frac{1}{2} m v^2 \] The radius \( R \) of the circular path is related to the velocity \( v \) by: \[ R = \frac{mv}{qB} \] Since the energy becomes three times the original, the velocity must increase by a factor of \( \sqrt{3} \). Therefore, the new radius is: \[ R_{\text{new}} = 3R \]
Step 2: Conclusion.
Thus, the correct answer is (C) \( 3R \).