Question

Anelectron emitted by a heated cathode and accelerated through apotential difference of 2.0 kV, enters a region with uniform magneticfield of 0.15 T. Determine the trajectory of the electron if thefield (a) is transverse to its initial velocity, (b) makes an angleof 30º with the initial velocity.

Answer 1

Magnetic fieldstrength, B = 0.15 T

Charge on the electron,e = 1.6 × 10⁻¹⁹C

Mass of the electron, m= 9.1 × 10⁻³¹ kg

Potential difference, V= 2.0 kV = 2 × 10³V

Thus, kinetic energy ofthe electron = eV

Where,

v = velocity ofthe electron

(a) Magnetic force on the electron provides the requiredcentripetal force of the electron. Hence, the electron traces acircular path of radius r.

Magneticforce on the electron is given by the relation,

Bev

Centripetalforce

Fromequations (1) and (2), we get

Hence,the electron has a circular trajectory of radius 1.0 mm normal to themagnetic field.

(b) When the field makes an angle θ of 30° with initialvelocity, the initial velocity will be,

Fromequation (2), we can write the expression for new radius as:

Hence,the electron has a helical trajectory of radius 0.5 mm along themagnetic field direction.