91Ó°ÊÓ

The magnetic field is uniform in all six regions.

Use the equation of magnetic force to find the direction of the magnetic field.

Right Hand Rule states that if we arrange our thumb, forefinger and middle finger of the right-hand perpendicular to each other, then the thumb points towards the direction of the motion of the conductor relative to the magnetic field, the forefinger points towards the direction of the magnetic field and the middle finger points towards the direction of the induced current.

Formulae are as follow:

$F=q\left(\stackrel{→}{v}×\stackrel{→}{B}\right)=qvB\sin \mathrm{θ}$

Where, F is magnetic force, v is velocity, B is magnetic field, q is charge of particle.

From the diagram, the particle is deflected towards the plate with a higher potential. Hence the particle must be a negatively charged particle.

In region (a):

The particle travels a half circle, and the force acting on the particle is in the right direction, and the velocity of the particle is upward. Using the right-hand rule, the magnetic field is in the inward direction to the plane of the paper.

In region (b)

The force acting on the particle is towards the right, and the velocity is downward. Using the right-hand rule, the direction ofthemagnetic field is outward.

In region (c)

The direction of the magnetic field is outward because the centripetal force acting on the particle is towards the left, and velocity is upward.

In region (d)

The force is upwards, and the velocity is towards left. Using the right-hand rule, the magnetic field is in the inward direction.

In region (e)

The direction of the magnetic field is inward because the force acting on the particle is downward, and velocity is towards the right.

In region (f)

The velocity direction is downward. The force acts to the right. So, the direction of the magnetic field is out of the page.

Hence, in region a, d, and e, the magnetic field goes into the plane, and in regions b, c, and f, it is out of the plane.