# An electron moves at a speed of 1.9 * 10 ^ 7 m / s perpendicular to a uniform magnetic field with an induction

**An electron moves at a speed of 1.9 * 10 ^ 7 m / s perpendicular to a uniform magnetic field with an induction of 9.1 * 10 ^ -5 T. Find the force acting on the electron and the radius of the circle along which it moves.**

V = 1.9 * 10 ^ 7 m / s.

∠α = 90 “.

B = 9.1 * 10 ^ -5 T.

m = 9.1 * 10 ^ -31 kg.

q = 1.6 * 10 ^ -19 Cl.

Fl -?

R -?

The electric charge q, which moves at a speed V in a magnetic field with induction B, is acted upon by the Lorentz force Fl: Fl = q * V * B * sinα, where ∠α is the angle between V and B.

Fl = 1.6 * 10 ^ -19 C * 1.9 * 10 ^ 7 m / s * 9.1 * 10 ^ -5 T * sin90 “= 27.66 * 10 ^ -17 N.

Fl = m * a – 2 Newton’s law, where a – centripetal acceleration.

a = V ^ 2 / R.

Fl = m * V ^ 2 / R.

R = m * V ^ 2 / Fl.

R = 9.1 * 10 ^ -31 kg * (1.9 * 10 ^ 7 m / s) ^ 2 / 27.66 * 10 ^ -17 H = 1.2 m.

Answer: Fl = 27.66 * 10 ^ -17 N, R = 1.2 m.