Having passed a potential difference of 2000 V, the electron flies into a uniform magnetic

| September 24, 2021 | education

Having passed a potential difference of 2000 V, the electron flies into a uniform magnetic field with an induction of 0.15 mT perpendicular to the lines of induction. Find the radius of the circle described by the electron.

U = 2000 V.

B = 0.15 mT = 15 * 10 ^ -5 T.

q = 1.6 * 10 ^ -19 Cl.

∠α = 90 °.

m = 9.1 * 10 ^ -31 kg.

R -?

Let’s find the speed of an electron when it enters a magnetic field.

q * U = m * V ^ 2/2.

V = √ (2 * q * U / m).

V = √ (2 * 1.6 * 10 ^ -19 C * 2000 V / 9.1 * 10 ^ -31 kg) = 26.5 * 10 ^ 6 m / s.

An electron in a magnetic field 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 = V ^ 2 / R.

m * V ^ 2 / R = q * V * B * sinα.

R = m * V ^ 2 / q * V * B * sinα = m * V / q * B * sinα.

R = 9.1 * 10 ^ -31 kg * 26.5 * 10 ^ 6 m / s * sin90 ° / 1.6 * 10 ^ -19 C * 15 * 10 ^ -5 T = 1 m.

Answer: the radius of motion of the electron was R = 1 m.



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