Question

A source injects an electron of speed v = 2.9 × 107 m/s into a uniform magnetic field of magnitude B = 1.7 × 10-3 T. The velocity of the electron makes an angle θ = 8.4° with the direction of the magnetic field. Find the distance d from the point of injection at which the electron next crosses the field line that passes through the injection point.

Answer 1

r = 0.664 m.

Step-by-step explanation:

Let's write the equation of the magnetic force, the blacks syndicate vectors

F = q v x B

From this expression we see that the force is perpendicular to the velocity and the field, so it is a centripetal force, the modulus of the force is

F = q v B sinT

We write Newton's second law

F = m a

a = v² / r

q v B sinT = m v² / r

r = m v / (q B sinT)

Let's calculate

r = 9.1 10-31 2.9 107 / (1.6 10-19 1.7 10-3 sin8.4)

r = 26.4 10-24 / 0.3973 10-22

r = 0.664 m

This is the distance from where the electron penetrates