Question

A charged particle is moving in a uniform magnetic field \( \vec{B} \) with a constant speed \( v \) in a circular path of radius \( r \). Which of the following graphs represents the variation of radius of the circle, with the magnitude of magnetic field \( \vec{B} \)?

• A. A
• B. B
• C. C
• D. D

Hint:

Remember, for a charged particle moving in a magnetic field, the radius of the circular path is inversely proportional to the magnetic field strength.

Answer 1

The Correct Option is B

The radius of the circular path \( r \) of a charged particle moving in a magnetic field is related to the magnetic field \( B \) by the following equation: \[ r = \frac{mv}{qB} \] where:
- \( m \) is the mass of the particle,
- \( v \) is the velocity of the particle,
- \( q \) is the charge of the particle,
- \( B \) is the magnetic field strength.
From the equation, we can see that \( r \) is inversely proportional to \( B \). As \( B \) increases, \( r \) decreases, which means the graph representing this relationship should show a decreasing radius as the magnetic field strength increases. Thus, the correct graph is option (B). Final Answer: (B)