An electron moves in a uniform magnetic field with an induction of 2 T.

An electron moves in a uniform magnetic field with an induction of 2 T. The trajectory of its motion is a helix with a radius of 10 cm. Determine the kinetic energy of the electron.

B = 2 T.

R = 10 cm = 0.1 m.

m = 9.1 * 10-31 kg.

q = 1.6 * 10-19 Cl.

∠α = 90 °.

Ek -?

The kinetic energy of the electron Ek is determined by the formula: Ek = m * V ^ 2/2, m is the mass of the electron, V is the speed of its movement.

The Lorentz force acts on the electron: Fl = q * V * B * sinα.

m * a = Fl.

a = V ^ 2 / R.

m * V ^ 2 / R = q * V * B * sinα.

m * V / R = q * B * sinα.

V = R * q * B * sinα / m.

Ek = m * (R * q * B * sinα) ^ 2/2 * m2 = (R * q * B * sinα) ^ 2/2 * m.

Ek = (0.1 m * 1.6 * 10-19 Cl * 2 T * sin90 °) ^ 2/2 * 9.1 * 10-31 kg = 5.6 * 10-10 J.

Answer: Ek = 5.6 * 10-10 J.