Question

The figure shows a convex lens of focal length 12 cm lying in a uniform magnetic field B of magnitude 1.2 T parallel to its principal axis. A particle with charge 2.0 × 10−3 C and mass 2.0 × 10−5 kg is projected perpendicular to the plane of the diagram with a speed of 4.8 m s−1. The particle moves along a circle with its centre on the principal axis at a distance of 18 cm from the lens. Show that the image of the particle moves along a circle and find the radius of that circle.
Figure

Answer 1

Explanation:

Convex lens focal length = 12 cm

Particle’s charge, q = 2.0 × $10^{-3}$ C

Mass, m = 2.0 × $10^{-5}$ kg

Uniform magnetic field, B = 1.2 T

Particle’s speed, v = 4.8 $ms^{-1}$

From the lens, the particle distance = 18 cm

Step 1:

According to the information provided, the object is anticipated perpendicular to the paper plane.

Let the circle’s radius on which the body is moving be r.

We understand that r = mvqB

r = 4 cm

Now, object distance, u = -18 cm

When the lens equation is used,

1v-1u = 112

Image distance, v = 36 cm.

Step 2:

Let the image’s circular path radius be r.

Thus, magnification is given as

vu = 8 cm

Therefore, the circular path radius in which the object moves is 8 cm.