Α – a particle with a velocity of 10 m / s flew into a uniform magnetic field, the induction of which is 0.3 T.

Α – a particle with a velocity of 10 m / s flew into a uniform magnetic field, the induction of which is 0.3 T. The particle velocity is perpendicular to the direction of the magnetic induction lines. Find the radius of the circle along which the particle will move and the period of revolution.

V = 10 ^ 6 m / s.

B = 0.3 T.

∠α = 90 °.

m = 6.64 * 10 ^ -27 kg.

q = 3.2 * 10 ^ -19 Cl.

R -?

T -?

An α-particle having a charge q, which moves at a speed V in a magnetic field with induction B, is acted upon 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 vector of magnetic induction B.

m * a = q * V * B * sinα – 2 Newton’s law.

The centripetal acceleration a is expressed by the formula: a = V2 / R.

m * V2 / R = q * V * B * sinα.

The radius of the circle R will be expressed by the formula: R = m * V / q * B * sinα.

R = 6.64 * 10 ^ -27 kg * 10 ^ 6 m / / 3.2 * 10 ^ -19 C * 0.3 T * sin90 ° = 0.07 m.

T = 2 * P * R / V.

T = 2 * 3.14 * 0.07 m / 10 ^ 6 m / s = 0.43 * 10 ^ -6 s.

Answer: R = 0.07 m, T = 0.43 * 10-6 s.