In the direction perpendicular to the lines of induction, an electron flies into the magnetic field at a speed of 10 Mm / s

In the direction perpendicular to the lines of induction, an electron flies into the magnetic field at a speed of 10 Mm / s, the circle of what radius did the electron describe if the field induction is 10 mT?

m = 9.1 * 10 ^ -31 kg.

q = 1.6.10 ^ -19 Cl.

∠α = 90 °.

V = 10 Mm / s = 10 * 10 ^ 6 m / s.

B = 10 mT = 10 * 10 ^ -3 T.

R -?

A moving charged particle in a magnetic field is affected by the Lorentz force, which is determined by the formula: Fl = q * V * B * sinα, where q is the particle charge, V is the speed of motion, B is the magnetic induction of the field, ∠α is the angle between B and V …

Let’s write 2 Newton’s law: m * a = Fl.

We express the centripetal acceleration by the formula: a = V ^ 2 / R, where R is the radius of the circle of motion.

m * V ^ 2 / R = q * V * B * sinα.

R = m * V / q * B * sinα.

R = 9.1 * 10 ^ -31 kg * 10 * 10 ^ 6 m / s / 1.6.10 ^ -19 C * 10 * 10 ^ -3 T * sin90 ° = 5.7 * 10 ^ -3 m.

Answer: the electron will describe a circle with a radius of R = 5.7 * 10 ^ -3 m.