Question

Answer the following questions:

(a) 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?

(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 setup to prevent the electron from deflecting from its straight line path.

Answer 1

$\left(a\right)$

As the particle travels undeflected through the magnetic field it means that the particle moves parallel to the magnetic field present in the region. So, the initial velocity of the particle will be parallel or anti-parallel to the field.

$\left(b\right)$

The magnetic field present in the region affects the direction of motion of the particle but it doesn't affect the magnitude of the speed of the particles. So, it is fairly [possible that the particle comes out with the same speed as the initial speed with which it enters the field.

$\left(c\right)$

The electron moves undeflected through the field if the electric force acts on the electron is equal and opposite to the magnetic field. Using the Fleming's left-hand rule, the magnetic field should be applied in the vertically downward direction.