An electron moves in a vacuum in a uniform magnetic field with an induction of 5 mT, its speed is 10 to the power of 4 km / s

| January 13, 2021 | education

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

m = 9.1 * 10 ^ -31 kg.
q = 1.6 * 10 ^ -19 Cl.
B = 5 mT = 5 * 10 ^ -3 T.
V = 104 km / s = 10 ^ 7 m / s.
∠α = 90 °.
r -?
The moving electron in a magnetic field is affected by the Lorentz force F: F = q * V * B * sinα.
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 = V2 / 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 moves in a circle with a radius of r = 0.011 m.



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