What is the radius of a circle described by an electron in a magnetic field if the modulus of the magnetic

| August 13, 2021 | education

What is the radius of a circle described by an electron in a magnetic field if the modulus of the magnetic field induction vector is 0.4T, and the electron’s velocity is 6.4 * 10 ^ 6m / s?

B = 0.4 T.

V = 6.4 * 10 ^ 6 m / s.

q = 1.6 * 10 ^ -19 Cl.

m = 9.1 * 10 ^ -31 kg.

R -?

An electric charge q moving at a speed V in a magnetic field with induction B is acted upon by the Lorentz force Flor, the value of which is determined by the formula: Flor = q * V * B.

2 Newton’s law for an electron will be: m * a = q * V * B.

Centripetal acceleration, and we will express it by the formula: a = V ^ 2 / R, where V is the speed of the electron, R is the radius of the circle.

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

m * V / R = q * B.

R = m * V / q * B.

R = 9.1 * 10 ^ 31 kg * 6.4 * 10 ^ 6 m / s / 1.6 * 10 ^ -19 C * 0.4 T = 91 * 10 ^ -6 m.

Answer: an electron describes a circle with a radius of R = 91 * 10 ^ -6 m.



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