Question

Figure (34-E17) shows a convex lens of focal length 12cm lying in a uniform magnetic field B of magnitude 1.2T parallel to its principal axis. A particle having a charge 2.0 x 10^-5C and mass 2.0 x 10^-5kg is projected perpendicular to the plane of the diagram with a speed of 4.8m/s. The particle moves along a circle with its centre on the principal axis at a distance of 18cm from the lens. Show that the image of the particle goes along a circle and find the radius of that circle.

Answer 1

The object will make a circular path, perpendicular to the plance of paper

Let the radius of the object be r

Here object distance K = 18cm.

Let the radius of the circular path of image = r'

So magnification = v/u = r'/r(magnetic path = image height/object height)

Hence radius of the circular path in which the image moves is 8cm.