# An electron moves in a magnetic field with an induction of 1 mT along a circle

An electron moves in a magnetic field with an induction of 1 mT along a circle with a radius of 0.5 cm, which is the kinetic energy of the electron.

m = 9.1 * 10 ^ -31 kg.

q = 1.6 * 10 ^ -19 Cl.

B = 1 mT = 1 * 10 ^ -3 T.

r = 0.5 cm = 5 * 10 ^ -3 m.

Ek -?

The kinetic energy of a body Ek of mass m, which moves with a speed V, is determined by the formula: Ek = m * V ^ 2/2.

The electron is acted upon by the Lorentz force F: F = q * V * B.

m * a = q * V * B – 2 Newton’s law.

We write the centripetal acceleration a according to the formula: a = V ^ 2 / r.

m * V2 / r = q * V * B.

V = q * B * r / m.

Ek = m * (q * B * r) ^ 2/2 * m ^ 2 = (q * B * r) ^ 2/2 * m.

Ek = (1.6 * 10 ^ -19 Kl * 1 * 10 ^ -3 T * 5 * 10 ^ -3 m) 2/2 * 9.1 * 10 ^ -31 kg = 3.5 * 10 ^ – 19 J.

Answer: the electron has kinetic energy Ek = 3.5 * 10 ^ -19 J.

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