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 set up to prevent the electron from deflecting from its straight line path.

Answer 1

a)

The magnetic field in a chamber has a constant direction but varies in magnitude from point to point. So a charged particle that has velocity either parallel or anti-parallel to the magnetic field will travel along a straight path.

Thus, the particle will travel without any deflection in the field.

b)

The magnetic force can change the direction of velocity of the particle but the magnitude of the particle will not change. So, the final speed of the charged particle will be equal to the initial speed of the charged particle.

c)

The direction of uniform electrostatic field in a chamber is the north-south direction and an electron that is travelling from west to east enters the chamber. If the electric force acting on the electron is equal and opposite of magnetic field then the moving electron will not be deflected.

The direction of magnetic force is towards the south and according to Fleming’s left hand rule, the direction of magnetic field should be in a vertically downward directions.