# An electron flies into a uniform magnetic field with an induction of 0.085 T at a speed of 4.6 * 10 ^ 7 m / s

**An electron flies into a uniform magnetic field with an induction of 0.085 T at a speed of 4.6 * 10 ^ 7 m / s directed perpendicular to the lines of magnetic induction. Determine the force acting on an electron in a magnetic field, and the radius of the circular arc along which it moves. The movement takes place in a vacuum.**

B = 0.085 T.

V = 4.6 * 10 ^ 7 m / s.

∠α = 900.

q = 1.6 * 10 ^ -19 Cl.

m = 9.1 * 10 ^ -31 kg.

Flor -?

R -?

A moving charge in a magnetic field is acted upon by the Lorentz force Flor, the value of which is determined by the formula: Flor = q * V * B * sinα, where q is the magnitude of the particle charge, V is the velocity of motion, B is the magnetic induction of the field, ∠α is the angle between the velocity motion V and magnetic induction B.

Flor = 1.6 * 10 ^ -19 C * 4.6 * 10 ^ 7 m / s * 0.085 T * sin90 = 6256 * 10 ^ -16 N.

Flor = m * a.

a = V ^ 2 / R.

q * V * B * sinα = m * V ^ 2 / R.

R = m * V / q * B * sinα.

R = 9.1 * 10 ^ -31 kg * 4.6 * 10 ^ 7 m / s / 1.6 * 10 ^ -19 C * 0.085 T * sin90 = 0.00307 m.

Answer: Flor = 6256 * 10-16 N, R = 0.00307 m.