# An electron moves in a vacuum in a uniform magnetic field with an induction of 5 mT

An electron moves in a vacuum in a uniform magnetic field with an induction of 5 mT, its speed is 10 ^ 4 km / s and is directed perpendicular to the lines of induction. Determine the radius of the circle along which it moves.

q = 1.6 * 10 ^ -19 Cl.

m = 9.1 * 10 ^ -31 kg.

B = 5 mT = 5 * 10 ^ -3 T.

V = 104 km / s = 10 ^ 7 m / s.

∠α = 90 °.

G – ?

A charged particle moving at a speed V, which is an electron, in a magnetic field with induction B is acted upon by the Lorentz force Fl, the value of which is expressed by the formula: Fl = q * V * B * sinα, where q is the electron charge, ∠α is the angle between the velocity the motion of the electron V and the vector of magnetic induction B.

Let’s write 2 Newton’s law: m * a = q * V * B * sinα.

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

m * V ^ 2 / g = q * V * B * sinα.

The radius of the circle of the trajectory of the electron will be determined by the formula: r = m * V ^ 2 / q * V * B * sinα = m * V / q * B * sinα.

r = 9.1 * 10 ^ -31 kg * 10 ^ 7 m / s / 1.6 * 10 ^ -19 C * 5 * 10 ^ -3 T * sin90 = 0.0114 m.

Answer: the radius of the trajectory of the motion of the electron will be r = 0.0114 m.

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