Question

A positively charged particle has been projected towards the east. It is deflected towards the north by a magnetic field. The field may be:
A. Towards west
B. Towards south
C. Upwards
D. Downwards

Answer 1

Hint: Consider a plane with the directions marked. Then apply Fleming’s left-hand rule and then stretch your fingers of the left hand according to the directions given in the question to get the direction of the magnetic field.

Complete step by step answer:
We have been given that the particle has been projected towards the east and after deflection moves toward the north and we need to find out the direction of the magnetic field.
We will have to use Fleming's left-hand rule, according to which if we place the thumb, middle finger and forefinger such that all three are mutually at right angles to each other. Then the thumb points towards the direction of the magnetic force, the forefinger points towards the magnetic field direction and the middle finger points towards the direction of the magnetic field. This can better be understood by the diagram below.

Here, two directions of current are possible according to the final direction of the particle; it can be upwards or towards east. But, if we consider the flow of current in an upward direction, then the angle between the velocity vector and magnetic field vector will become zero and the particle will not experience any force. Mathematically this denoted as,
$\vec{F}=q\vec{v}\times \vec{B}=qBvsin\theta$
Where $\theta$ is the angle between the velocity vector of the particle and the magnetic field.

Therefore, we will consider the direction of the current flow towards the east. Now, the situation given in this question can be solved using the three fingers of our own hand. If we point our thumb towards the north, our middle finger towards the east, then we will be able to see that the forefinger is pointing in the downward direction.
Hence, option D is the correct answer.

Note:
The choice of the direction of current can be either towards east or upwards. We should check it from the formula of force acting on a particle in a magnetic field by a current-carrying conductor. If we take the direction of current upwards by mistake, then the direction of the magnetic field will become east which will be wrong.