Question

The radius of the circular path of a charged particle in a uniform magnetic field is directly proportional to the:

• A. charge of the particle
• B. momentum of the particle
• C. intensity of the magnetic field
• D. energy of the particle

Hint:

The radius of the circular path of a charged particle in a magnetic field depends on its momentum and the strength of the magnetic field.

Answer 1

The Correct Option is B

Step 1: Formula for the Radius of the Circular Path.
The radius \( r \) of the circular path of a charged particle in a magnetic field is given by: \[ r = \frac{mv}{qB} \] where \( m \) is the mass of the particle, \( v \) is the velocity, \( q \) is the charge, and \( B \) is the magnetic field strength.
Step 2: Analyzing the Proportionality.
We can express momentum \( p \) as \( p = mv \), so the radius becomes: \[ r = \frac{p}{qB} \] Therefore, the radius is directly proportional to the momentum \( p \) of the particle.
Step 3: Conclusion.
Hence, the correct answer is (B) momentum of the particle.