An electron moves in a vacuum in a uniform magnetic field with an induction of 5 • 10 ^ -3 T; its speed is 1.0 • 10 ^ 4 km / s

| July 3, 2021 | education

An electron moves in a vacuum in a uniform magnetic field with an induction of 5 • 10 ^ -3 T; its speed is 1.0 • 10 ^ 4 km / s and is directed perpendicular to the lines of magnetic induction. Determine the force acting on the electron and the radius of the circle along which it moves.

m = 9.1 * 10 ^ -31 kg.

q = 1.6 * 10 ^ -19 Cl.

B = 5 * 10 ^ -3 T.

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

∠α = 90 °.

Flor -?

r -?

A moving electric charge in a magnetic field is acted upon by the Lorentz force Flor: Flor = q * V * B * sinα, where q is the magnitude of the charge, V is the speed of the charge, B is the magnetic induction of the field, ∠α is the angle between V and B.

Flor = 1.6 * 10 ^ -19 C * 10 ^ 7 m / s * 5 * 10 ^ -3 T * sin90 ° = 8 * 10 ^ -15 N.

Let’s write 2 Newton’s law for an electron in a magnetic field: m * a = q * V * B * sinα.

Since the electron moves in a circle, it moves with a centripetal acceleration a: a = V ^ 2 / r.

m * V ^ 2 / r = q * V * B * sinα.

m * V / r = q * B * sinα.

The radius of the circle r will be determined by the formula: r = 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 ° = 0.011 m.

Answer: the electron is acted upon by the force Flor = 8 * 10 ^ -15 N, it moves in a circle with a radius of r = 0.011 m.



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