The period of electron revolution in a uniform magnetic field with an induction of 5.6TL is 6 ns.

| September 9, 2021 | education

The period of electron revolution in a uniform magnetic field with an induction of 5.6TL is 6 ns. The radius of the circle described by the electron is 1 cm. Determine: the speed of the electron: the force acting on the electron from the side of the magnetic field.

T = 6 ns = 6 * 10-9 s.

B = 5.6 T.

q = 1.6 * 10-19 Cl.

∠α = 90 °.

R = 1 cm = 0.01 m.

m = 9.1 * 10-31 kg.

V -?

Fl -?

In a magnetic field, the electron is acted upon by the Lorentz force Fl: Fl = q * V * B * sinα.

m * a = q * V * B * sinα – 2 Newton’s law.

The centripetal acceleration a is expressed by the formula: a = V2 / R.

m * V2 / R = q * V * B * sinα.

The electron velocity V is expressed by the formula: V = q * B * sinα * R / m.

V = 1.6 * 10-19 C * 5.6 T * sin90 ° * 0.01 m / 9.1 * 10-31 kg = 0.008 * 1012 m / s.

Fl = 1.6 * 10-19 C * 5.6 T * sin90 ° * 0.008 * 1012 m / s = 0.07 * 10-7 N.

Answer: the speed of the electron is V = 0.008 * 1012 m / s, the Lorentz force acts on the electron Fl = 0.07 * 10-7 N.



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