An electron flies into a uniform magnetic field with an induction of 90 mT perpendicular to the lines of magnetic

| September 11, 2021 | education

An electron flies into a uniform magnetic field with an induction of 90 mT perpendicular to the lines of magnetic induction at a speed of 4000 km / s What is the radius of its trajectory

B = 90 mT = 0.09 T.

q = 1.6 * 10-19 Cl.

∠α = 90 °.

V = 4000 km / s = 4000000 m / s.

m = 9.1 * 10-31 kg.

R -?

Since an electron is a charged particle with a charge q = 1.6 * 10-19 C and a mass m = 9.1 * 10-31 kg, then in a magnetic field it is acted upon by the Lorentz force Fl and Newton’s 2 law is valid.

Fl = q * V * B * sinα.

m * a = q * V * B * sinα.

We express the centripetal acceleration by the formula: a = V2 / R.

m * V2 / R = q * V * B * sinα.

R = m * V * sinα / q * B.

R = 9.1 * 10-31 kg * 4000000 m / s * sin90 ° / 1.6 * 10-19 C * 0.09 T = 0.00025 m.

Answer: in a magnetic field, the radius of the trajectory is R = 0.000025 m.



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