Question

A charged particle enters a magnetic field H with its initial velocity making an angle of \[45^\circ \]with H. The path of the particle will be
A. A straight line
B. A circle
C. An ellipse
D. A helix

Answer 1

Hint:When the charged particle enters a magnetic field then the magnetic field applies force on the charged particle which changes the path of the motion of the charged particle. The magnetic force is perpendicular to the velocity of the charged particle.

Formula used:
\[\overrightarrow F = q\left( {\vec v \times \vec B} \right)\]
Here \[\vec F\] is the magnetic force vector, \[\vec v\] is the velocity of the charged particle and \[\vec B\] is the magnetic field in the region.

Complete step by step solution:
It is given that the charged particle enters into the region of the magnetic field with magnetic field strength H. The velocity of the charged particle is making an angle of \[45^\circ \].

As the initial velocity is making an angle with the magnetic field, so there are two components of the initial velocity of the charged particle, one is perpendicular to the magnetic field and other is horizontal component. As the magnetic force is proportional to the vector product of the velocity and the magnetic field, so the horizontal component will not experience the magnetic force and it remains constant.

The perpendicular component of the force will cause the circular path of the motion and the horizontal velocity component will make the charged particle move forward making a circular revolution. So, the path of the motion of the charged particle will be circular motion in the vertical plane and linear in the horizontal plane, i.e. the path will be helix.

Therefore, the correct option is D.

Note: We should note that the separation between the two helical rings will be equal to the linear distance covered by the charged particle within a period of revolution. If velocity is perpendicular to the magnetic field then the path will be circular.