A charged particle, having passed the accelerating potential difference U = 7.2 kV, moves in a uniform magnetic

| June 25, 2021 | education

A charged particle, having passed the accelerating potential difference U = 7.2 kV, moves in a uniform magnetic field with induction B = 15 mT along a circle of radius R = 1 cm. Determine the specific charge of the particle and its velocity.

U = 7.2 kV = 7200 V.
B = 15 mT = 0.015 T.
R = 1 cm = 0.01 m.
q / m -?
The specific charge of a particle is the charge calculated per unit mass of charge q / m.
With the passage of the potential difference, the electric field did the work A = q * U.
The work of the electric field went A to increase the kinetic energy of the charge Ek = m * V ^ 2/2.
q * U = m * V ^ 2/2.
q / m = V ^ 2/2 * U.
In a magnetic field, the Lorentz force Flor = q * B * V acts on the charge.
Let’s write 2 Newton’s law: m * a = q * B * V.
Centripetal acceleration is determined by the formula: a = V ^ 2 / R.
m * V ^ 2 / R = q * B * V.
m * V / R = q * B.
m * V / R = q * B.
q / m = V / R * B.
V ^ 2/2 * U = V / R * B.
V = 2 * U / R * B.
V = 2 * 7200 V / 0.015 T * 0.01 m = 96 * 10 ^ 6 m / s.
q / m = 96 * 10 ^ 6 m / s / 0.015 T * 0.01 m = 640 * 10 ^ 9 C / kg.
Answer: the specific charge of a particle is q / m = 640 * 10 ^ 9 C / kg.



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