A particle of mass m and charge q is projected into a region having a perpendicular magnetic field B. Find the angle of deviation figure of the particle as it comes out of the magnetic field if the width d of the region is very slightly smaller than

(a) (b).

(c)

Given-

Mass of the particle = m

Charge of the particle = q

Perpendicular magnetic field = B

To find the angle of deviation figure of the particle as it comes out of the magnetic field when -

(a) When the width,

d is equal to the radius

θ is the angle between the radius and tangent drawn to the circle , which is equal to.

(b) When the width,

Now, in this case, the width of the region in where magnetic field is applied is half of the radius of the circular path.

As the magnetic force is acting only along the y –axis,the velocity of the particle will remain constant along the x-axis.

So, if d distance is travelled along the x axis,

then,

where,

v=velocity

t=time

for constant velocity the acceleration along the x direction is zero.

Hence the force will act only along the y direction.

Using the 3^rd equation of motion along the y axis-

where

u = initial velocity

a = acceleration

t= time taken

since, initial velocity is 0

Also, as θ = 90⁰

From (1)

We know

From above fig.

(c) When the width, d =

From above fig., it can be concluded that the angle between the initial direction and final direction of velocity is .