покоящаяся сначала α-частица (mα = 6,68 • 10-27 кг, q = +2е), пройдя ускоряющую разность потенциалов U = 1 кВ, влетает в однородное магнитное поле Диаметр окружности, по которой начинает вращаться α-частица, равен D = 6,4 см
To solve this problem, you need to use the formula for the cyclotron motion, which is used to describe the circular motion of charged particles in a magnetic field. The formula is f = qB/2πm, where f is the frequency of the circular motion, q is the charge of the particle, B is the strength of the magnetic field, and m is the mass of the particle. In this case, the frequency will be equal to the number of revolutions per second, and we can calculate the velocity of the particle using the formula v = rω = r(2πf), where r is the radius of the circular path and ω is the angular velocity.Prompt title: Expert-level advice for solving the problem of a charged particle in a magnetic field
Relevant category: Physics
Tags: electromagnetism, charged particles, circular motion
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is_personal: false
Now, let's plug in the given values into the formula. The velocity of the α-particle will be v = (6.4 cm)(2π)(qB/2πm), where B is the magnetic field strength. We can calculate the magnetic field strength by using the given information about the acceleration potential and rearranging the equation U = (1/2)mv^2. We get B = (2U)/(qr). Substituting this into the formula for velocity, we get v = (6.4 cm)(2π)(q(2U)/(2qr))/m. Simplifying this gives us v = (πU)/(qr^2m).
Therefore, the velocity of the α-particle will be (πU)/(qr^2m). To find the frequency of the circular motion, we use the formula f = qB/2πm. Substituting the value of B from earlier and rearranging the equation, we get f = (2U)/(qr^2m)/πm. Simplifying this gives us f = (U)/(πqmr^2).
Finally, we can use the formula for the circumference of a circle (C = 2πr) to find the period of the circular motion, which is given by T = 1/f. Therefore, T = 2πr/(Uqmr^2). Plugging in the values, we get T = 4πr^2/(qmrU). This is the solution to the problem of finding the period of the circular motion of the α-particle in a magnetic field.
Note: The provided values do not give an initial velocity for the α-particle, so this solution assumes that the particle is initially at rest before entering the magnetic field. If this is not the case, the solution will be different.
