An electron flies into a uniform magnetic field with induction B = 2mT perpendicular to the lines of magnetic

An electron flies into a uniform magnetic field with induction B = 2mT perpendicular to the lines of magnetic field induction. Determine the time T of one revolution of an electron and the number of revolutions of an electron in 1 second.

B = 2 mT = 2 * 10-3 T.

q = 1.6 * 10-19 Cl.

∠α = 90 °.

m = 9.1 * 10-31 kg.

t = 1 s.

T -?

n -?

The time of one complete revolution is called the period of rotation of the electron T.

T = L / V, where L is the circumference of one revolution, V is the electron rotation speed.

L = 2 * п * R.

T = 2 * п * R / V.

Since the electron is a charged particle, the Lorentz force Fl will act on it in a magnetic field: Fl = q * V * B * sinα.

2 Newton’s law will have the form: m * a = q * V * B * sinα – 2 Newton’s law.

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

m * V ^ 2 / R = q * V * B * sinα.

m * V / R = q * B * sinα.

V / R = q * B * sinα / m.

R / V = ​​m / q * B * sinα.

T = 2 * п * m / q * B * sinα.

T = 2 * 3.14 * 9.1 * 10-31 kg / 1.6 * 10-19 Cl * 2 * 10-3 T * sin90 ° = 17.86 * 10-9 s.

T = t / n.

n = t / T.

n = 1 s / 17.86 * 10-9 s = 55991041.

Answer: T = 17.86 * 10-9 s, n = 55991041.