Answer the following questions given

Answer the following questions :
(i) A magnetic field that varies in magnitude from point to point but has a constant direction (East to West) is set up in a chamber. A charged particle enters the chamber and travels undeflected along a straight path with constant speed. What can you say about the initial velocity of the particle?
(ii) A charged particle enters an environment of a strong and non-uniform magnetic field varying from point to point both in magnitude and direction, and comes out of it following a complicated trajectory. Would its final speed equal to the initial speed, if it suffered no collisions with the environment?
(iii) An electron travelling West to East enters a chamber having a uniform electrostatic field in North to South direction. Specify the direction in which a uniform magnetic field should be set up to prevent the electron from deflecting its straight line path.

(i)The magnetic field is in constant direction from East to West. According to the question, a charged
particle travels undeflected along a straight path with constant speed. It is only possible, if the magnetic force experienced by the charged particle is zero.
The magnitude of magnetic force on a moving charged particle in a magnetic field is given by F = qv B sin θ. (where θ is the angle between v and B). Here F = 0, if and only if sin θ = 0 (as v ≠ 0, q≠Q, B≠0). This indicates the angle between the velocity and magnetic field is 0° or 180°. Thus, the charged particle moves parallel or anti-parallel to the magnetic field B.

(ii) Yes, the final speed be equal to its initial speed as the magnetic force acting on the charged particle only changes the direction of velocity of charged particle but cannot change the magnitude of velocity of charged particle.
(iii) As, the electric field is from North to South, that means the plate in North is positive and in South is negative. Thus, the electrons (negatively charged) attract towards the positive plate that means move towards North. If we want that there should be no deflection in the path of electron, then the magnetic force should be in South direction.

By F = — e (v X B), the direction of velocity is West to East, the direction of force is towards South, by using the Fleming’s left hand rule, the direction of magnetic field (B) is perpendicularly inwards to the plane of paper.