Determine the radius of the circle and the period of revolution of the electron in a uniform magnetic field

| August 7, 2021 | education

Determine the radius of the circle and the period of revolution of the electron in a uniform magnetic field with induction B = 0.01 T. The electron velocity is perpendicular to the magnetic induction vector and is equal to m / s.

V = 106 m / s.

q = 1.6 * 10 ^ -19 Cl.

B = 0.01 T.

∠α = 90 °.

m = 9.1 * 10 ^ -31 kg.

R -?

T -?

The electric charge q, which moves at a speed V in a magnetic field with induction B, is affected by the Lorentz force Fl, the value of which is determined by the formula: Fl = q * V * B * sinα, where ∠α is the angle between the direction of motion of the charge V and the magnetic induction vector IN.

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

a = V ^ 2 / R.

m * V ^ 2 / R = q * V * B * sinα.

R = m * V / q * B * sinα.

R = 9.1 * 10 ^ -31 kg * 10 ^ 6 m / s / 1.6 * 10 ^ -19 C * 0.01 T * sin90 ° = 568.75 * 10 ^ -6 m.

T = S / V = 2 * п * R / V.

T = 2 * 3.14 * 568.75 * 10 ^ -6 m / 10 ^ 6 m / s = 0.00357 s.

Answer: R = 568.75 * 10 ^ -6 m, T = 0.00357 s.



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