# The electron moves at a speed of 1.76 * 10 ^ 6 m / s perpendicular to the induction vector of a uniform magnetic field.

**The electron moves at a speed of 1.76 * 10 ^ 6 m / s perpendicular to the induction vector of a uniform magnetic field. The radius of the circle along which the electron moves is 2.5 cm. Find the magnetic induction.**

q = 1.6 * 10 ^ -19 Cl.

m = 9.1 * 10 ^ -31 kg.

V = 1.76 * 10 ^ 6 m / s.

R = 2.5 cm = 0.025 m.

B – ?

A moving electron in a magnetic field is acted upon by the Lorentz force Fl, the value of which is determined by the formula: Fl = q * B * V.

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

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

m * V ^ 2 / R = q * B * V.

We express the magnetic induction B by the formula: B = m * V / R * q.

B = 9.1 * 10 ^ -31 kg * 1.76 * 10 ^ 6 m / s / 0.025 m * 1.6 * 10 ^ -19 Cl = 400 * 10 ^ -6 T.

Answer: the induction of the magnetic field is B = 400 * 10 ^ -6 T.