The electron flew into a uniform magnetic field, the induction of which is B = 200 μT, perpendicular to the lines of force and described an arc of a circle of radius r = 4 cm. Determine the kinetic energy of an electron.
q = 1.6 * 10 ^ -19 Cl.
m = 9.1 * 10 ^ -31 kg.
B = 200 μT = 200 * 10 ^ -6 T.
g = 4cm = 0.04 m.
∠α = 90 °.
The kinetic energy of an electron Ek is determined by the formula: Ek = m * V ^ 2/2, where m is the mass of the electron, V is the speed of motion of the electron.
The Lorentz force Fl acts on an electron in a magnetic field, so it moves in a circle with centripetal acceleration.
Let us express the Lorentz force by the formula: Fl = q * V * B * sinα, where ∠α is the angle between the direction of motion of the electron V and the vector of magnetic induction B.
m * a = q * V * B * sinα.
We express the centripetal acceleration a by the formula: a = V2 / r.
m * V2 / g = q * V * B * sinα.
V = r * q * B * sinα / m.
The formula for determining the kinetic energy of an electron Ek will take the form: Ek = (g * q * B * sinα) 2/4 * m.
Ek = (0.04 m * 1.6 * 10 ^ -19 C * 200 * 10 ^ -6 T * 1) 2/4 * 9.1 * 10 ^ -31 kg = 4.5 * 10 ^ -19 J.
Answer: the kinetic energy of an electron is Ek = 4.5 * 10 ^ -19 J.