Answer the following questions:
(a) A magnetic field that varies in magnitude from point but has a constant direction (east to west) is set up in a chamber. A charged particle enters the chamber and travles undeflected along a straight path with constant speed. What can you say about the initial velocity of the particle?
(b) 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 the initial speed if it suffered no collisions with the environment?
(c) 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 from its straight line path.

Explanation

(a) The force acting on a charged particle, moving in a magnetic field is, `F=qvBsintheta`. The charged particle will travel undeflected along a straight path with constant speed in a magnetic field if no force acts on it i.e. `F=0`. It will be so if `sin theta=0` i.e. `theta=0^@` or `180^@`. It means, the initial velocity `vecv` of charged particle is either parallel or antiparallel to magnetic field `vecB`.
(b) Yes, because the magnetic force acting on a charged particle moving in a magnetic field can change the direction of `vecv` and not its magnitude.
(c) When an electron travelling west to east is subjected to uniform electrostatic field acting north to south direction, the electron is deflected by the electric field towards north. The moving electron can remain undeflected only if the force acting on electron due to electric field is equal and opposite to that due to magnetic field. It means the magnetic field must deflect the electron towards south. The expression for magnetic Lorentz force on electron is, `vecF=-e(vecxxvecB)`. Thus the direction of `vecB`, according to Right hand screw rule or Fleming's left hand rule should be applied along vertical and in downward direction.