Question

An electron moving along the positive X axis with a velocity of 8 × 10⁷ ms⁻¹ enters a region having a uniform magnetic field B = 1.3 × 10⁻³ T along the positive Y axis.

1. Explain why the electron describes a circular path.
2. Calculate the radius of the circular path described by the electron.

Answer 1

a. Because the force exerted by the magnetic field is always perpendicular to the velocity of the electron. Hence, it provides the necessary centripetal force and the electron describes a circular path.

b. Magnetic force = Centripetal force

evB = `"mv"^2/r`

⇒ `e/m = v/(Br)`

`(1.6 xx 10^(-19))/(9.1 xx 10^(-31)) = (8 xx 10^7)/(1.3 xx 10^(-3) xx r)`

∴ r = 0.35 m