Question

Doubly-ionised helium ions are projected with a speed of 10 km s−1 in a direction perpendicular to a uniform magnetic field of magnitude 1.0 T. Find (a) the force acting on an ion (b) the radius of the circle in which it circulates and (c) the time taken by an ion to complete the circle.

Answer 1

Explanation:

Helium ions speed, v = 104 m/s

Uniform magnetic field, B = 1.0 T

Helium ions charge = 2e

Helion ions mass, m = 4$\times$1.6$\times$10-27 Kg

(a) On an ion, the acting force is,

F = qvBsinθ

= 3.2 $\times$ 10−15 N

(b) The circle’s radius in which it rotates,

r = mvqB= 2$\times$10-2310-19 = 2$\times$10-4 m

(c) To complete a circle, the time taken is,

T = 2πrv = 1.31 $\times$ 10−7 s