Question

When a positively charged particle enters into a uniform magnetic field with uniform velocity, its trajectory can be
(i) A straight line
(ii) A circle
(iii) A helix
A. (i) only
B. (i) or (ii)
C.(i) or (iii)
D. Any one of (i), (ii) and (iii)

Answer 1

To answer this problem, consider the equation for force on a moving charge in a magnetic field. It gives the relation between force, velocity and magnetic field. Then, consider different conditions for the direction of these parameters. These conditions will help to find the trajectory of the positively charged when it enters into the uniform magnetic field with uniform velocity.

Formula used:
$F = q({v \times B})$

Complete step-by-step answer:
We know, magnetic force on a moving charge in a magnetic field is given by,
$F = q({v \times B})$ …(1)
Where, q is the charge of the particle
V is the velocity of the particle
B is the magnetic field
The trajectory of the particle depends on the direction of magnetic field, velocity and force. There are three cases based on the direction of these parameters.
Case. i) When the particle moves along the direction of the magnetic field, then equation. (1) becomes,
$F= 0$
Thus, the particle moves in a straight line along the incident direction.
Case. ii) When the particle moves perpendicular to the direction of the magnetic field, the force becomes perpendicular to the direction of the field.
Thus, the trajectory of the particle is circular.
Case. iii) When the direction of velocity has both parallel and perpendicular components to the direction of magnetic field, the parallel component tends to move the particle along the direction of magnetic field. While the perpendicular component moves the particle in a circle.
Thus, the trajectory of the particle is helix.
Hence, when a positively charged particle enters into a uniform magnetic field with uniform velocity, its trajectory can be straight line or a circle or a helix.
So, the correct answer is option C i.e. Any one of (1), (ii) and (iii)

So, the correct answer is “Option D”.

Note: When the charged particle takes a helical trajectory, it may enter a region which has a non-uniform magnetic field. Suppose the particle is moving from a region with stronger magnetic field to a region with weaker magnetic field and then again to a region with stronger magnetic field. The particle may reflect back before entering the region with a stronger magnetic field. When the magnetic field is perpendicular to the velocity, it does not work on the charged particle whether positively charged particle or a negatively charged particle.