Question

Протон описал окружность радиусом 5 см в однородном магнитном поле с индукцией 20 мТл. Определите скорость протона. Чему равна работа силы, действующей на протон?

Answer 1

Скорость протона определяется формулой  v=q B R/(m)
откуда v=1,6 10^-19*0.02*0,05/(1.66 10^-27)=96385.5 м\с
На протон действует сила Лоренца: F=q v B sin(a)
т.к. сила перпендикулярна скорости, то сила Лоренца работы не совершает.
Ответ. А=0

Answer 2

Calculation of Proton's Velocity:

To determine the velocity of the proton, we can use the formula for the centripetal force acting on a charged particle moving in a magnetic field. The centripetal force is provided by the magnetic force acting on the proton.

The formula for the magnetic force on a charged particle moving in a magnetic field is given by:

F = qvB

Where: - F is the magnetic force, - q is the charge of the particle, - v is the velocity of the particle, and - B is the magnetic field strength.

In this case, the proton is moving in a circular path with a radius of 5 cm, and the magnetic field has an induction of 20 mT (millitesla), which is equivalent to 0.02 T (tesla).

Since the proton has a positive charge of +e (elementary charge), we can substitute the values into the formula and solve for the velocity.

F = qvB

qvB = mv^2/r

v = (qBr/m)^0.5

Now, let's calculate the velocity of the proton.

Using the values: - q = +e (elementary charge) = 1.6 x 10^-19 C (coulombs) - B = 0.02 T (tesla) - r = 5 cm = 0.05 m (meters) - m = mass of the proton = 1.67 x 10^-27 kg

v = (1.6 x 10^-19 C * 0.02 T * 0.05 m / 1.67 x 10^-27 kg)^0.5

Calculating the above expression gives us the velocity of the proton.