A proton and a deuteron are moving with equal velocities perpendicular to a uniform magnetic field. A deuteron has the same charge as the proton but has twice its mass. The ratio of the magnetic force on the proton to that on the deuteron is:

a. 0.5.
b. 1.
c. 2.
d. There is no magnetic force in this case.

option (b)

Explanation:

mass of proton, mp = m

mass of deuteron, md = 2m

charge on proton, qp = q

charge on deuteron, qd = q

The magnetic force on the charged particle when it is moving is given by

F = q v B Sinθ

where, θ is the angle between the velocity and magnetic field.

Here, θ = 90°

Let v is the velocity of both the particle when they enters in the magnetic field.

The force on proton is given by

Fp = q x v x B (1)

The force on deuteron is

Fd = q x v x B (2)

Divide equation (1) by equation (2)

Fp / Fd = 1

Thus, the ratio of force on proton to the force on deuteron is 1 : 1.

Thus, option (b) is correct.