Find the speed of a charged particle, which it acquired after passing an accelerating voltage of 8.7 kV

| August 15, 2021 | education

Find the speed of a charged particle, which it acquired after passing an accelerating voltage of 8.7 kV, if in a magnetic field with induction B = 0.12 T it describes a circle with a radius of R = 27 cm.

U = 8.7 kV = 8700 V.

B = 0.12 T.

R = 27 cm = 0.27 m.

V -?

In a magnetic field, a moving charged particle is acted upon by the Lawrence force Flor = q * V * B.

m * V ^ 2 / R = q * V * B – 2 Newton’s law.

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

The work of the electric field A = q * U is equal to the change in the kinetic energy of a charged particle ΔEk = m * V ^ 2/2: q * U = m * V ^ 2/2.

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

q * V * B * R = 2 * q * U.

V = 2 * U / B * R.

V = 2 * 8700 V / 0.12 T * 0.27 m = 537037 m / s.

Answer: the charged particle has acquired a velocity of V = 537037 m / s.



One of the components of a person's success in our time is receiving modern high-quality education, mastering the knowledge, skills and abilities necessary for life in society. A person today needs to study almost all his life, mastering everything new and new, acquiring the necessary professional qualities.