Question

The radius of curvature of the path of the charged particle in a uniform magnetic field is directly proportional to
A. The charge on the particle
B. The momentum of the particle
C. The energy of the particle
D. The intensity of the field

Answer 1

Hint:A magnetic field is the area around a magnet or moving charges where its force can be felt. The force due to a magnetic field will be calculated by Lorentz force. The expression of radius of the curvature is obtained by equating the Lorentz force and centripetal force.

Formula used:
The radius of the circular path will be mathematically written by the following formula:
\[r = \dfrac{{mv}}{{qB}}\] ……(i)
Where ‘m’ is the mass of the charge, ‘v’ is the velocity with which it is moving and ‘B’ is the magnetic field.

Complete step by step solution:
The force experienced by a charge due to a magnetic field can cause a charge to move in a spiral or circular path. This radius of the circular path will be mathematically written by the following formula:
\[r = \dfrac{{mv}}{{qB}}\] ……(i)

Also, since the charge is in motion, it will also have some momentum. The momentum of the charged particle is given as the product of mass of the particle and its velocity. It is represented by the letter ‘p’. Mathematically, it is written as,
p=mv
Therefore, equation (i) can be written as,
\[r = \dfrac{p}{{qB}}\]
Since the charge and magnetic field are constant, therefore the above equation can also be written as,
\[r \propto p\]
The radius of curvature of the path of the charged particle in a uniform magnetic field is directly proportional to the momentum of the particle.

Hence, option B is the correct answer.

Note: Since, the current will be passing through the conductor, an electric field will be produced. Also, since the conductor will start behaving as a magnet, the magnetic field will also be there. These electric and magnetic effects will create a force together also known as the Lorentz force which was first observed by Hendrik Antoon Lorentz in 1895.