Question

An electron (charge -e, mass m) enters a uniform magnetic field B=-Bok at A with a speed v, at an angle 37° and leaves the field at B with speed v (see figure). Then choose the correct statement(s).

Answer 1

Correct option is (3) and (4)

Magnetic force can only change the direction of velocity but do not change magnitude of velocity, as magnetic force is a type of centripetal force.

\(\frac {mv^2}{R} = qvB\)

⇒ R \(= \frac {mv_0}{eB_0}\)

From geometry, we can conclude that particle exits from the boundary with same magnitude as it enters into it, and also it leaves with the same angle with vertical, as it enters. It is shown in below figure, 

From the given figure, we can conclude that, 

∠OAB =∠OBA = \(\theta\) = 90° - 37° = 53°

Angle subtended at centre by AB is, ∠AOB = 180° - 2 x 53° = 74°

Triangle AOB is shown as below, 

From the triangle, we can conclude,

AB = 2Rsin37°

⇒ \(AB = 2 \frac {mv_0}{eB_0} \times \frac {3}{5}\)

⇒ AB = \(\frac {6mv_0}{5eB_0}\)