An electron moves in a circle in a uniform magnetic field with an induction of 0.1 T. Determine the force acting

| September 7, 2021 | education

An electron moves in a circle in a uniform magnetic field with an induction of 0.1 T. Determine the force acting on the electron from the field. The radius of the circle is 0.5 cm. The mass of the electron is 9.1 * 10 ^ -31 kg, the charge is -1.6 * 10 ^ -19 Cl.

B = 0.1 T.

r = 0.5 cm = 0.5 * 10 ^ -3 m.

m = 9.1 * 10 ^ -31 kg.

q = 1.6 * 10 ^ -19 Cl.

Fl -?

A moving charge in a magnetic field is affected by the Lorentz force, the value of which is determined by the formula: Fl = q * B * V, where q is the electric charge, B is the magnetic induction of the field, V is the speed of the charge.

Let’s write Newton’s 2 law: Fl = m * a.

Centripetal acceleration a is determined by the formula: a = V ^ 2 / r.

q * B * V = m * V ^ 2 / r.

V = √ (q * B * r / m).

Fl = q * B * √ (q * B * r / m).

Fl = 1.6 * 10 ^ -19 C * 0.1 T * √ (1.6 * 10 ^ -19 C * 0.1 T * 0.5 * 10 ^ -3 m / 9.1 * 10 ^ -31 kg) = 473.6 * 10 ^ -19 N.

Answer: a force Fl = 473.6 * 10 ^ -19 N. acts on the electron.



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