Answer the following questions:

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.

If the Charged particle have to go undeflected then there should be no force experienced by it, or resultant of all the forces on the particle is zero. Here, the charged particle is experiencing Magnetic Lorentz force and electrostatic force due to electric field

We know Magnetic Lorentz Force is given by

Direction of the Magnetic force is perpendicular to plane containing V and B. and for a positively charged particle can be found out with help of Fleming’s left hand thumb rule.

Electrostatic force is given by

F = qE

Where F is the force experienced by particle having charge q and moving in an electric field E, direction of force is same as that of Electric field for a positively charged particle and is exactly reversed in case of negatively charged particle.

So both the forces on particle should be equal in magnitude and opposite in direction.

Since Electric Field is from North to South, and particle is an electron i.e. negatively charged so force on it should be towards North so force due to magnetic field should be towards south .As shown in figure

Using the Fleming left hand rule we will decide the direction of magnetic field

Flemings rule : If the stretch our forefinger middle finger and thumb mutually perpendicular to each other then if forefinger depicts the direction of magnetic field, middle finger depicts the direction of the current(Direction of Velocity of Positive Charge) then, Thumb depicts the direction of Force.

Applying the rule

Since Electron is negatively charged and moving from West to east so direction of current is from east to west, depicted by middle finger, force should be towards both depicted by our thumb, so we find our forefinger depicting magnetic field is in a direction vertically downwards in the plane

Now equating magnitude of both the forces

Here θ = 90° because Velocity of particle is perpendicular to Magnetic field,

So,sinθ = 1

i.e.

or magnitude of magnetic field is given by

, in a direction vertically downwards.