A charged particle that has passed through an accelerating difference

Given a charged particle that has undergone acceleration at a potential difference of 4 kV. After this, it began to move in a uniform magnetic field with an induction of 20 mT in a circle with a radius of 2 cm. It is necessary to calculate the speed of this particle.

To solve the problem, you need to use the formula for centripetal acceleration:

a = v²/r

Where:

• a - centripetal acceleration of the particle
• v - particle speed
• r - radius of the circle along which the particle moves

To find the speed of a particle, you must first determine the centripetal acceleration. Since the particle moves in a uniform magnetic field, it is acted upon by the Lorentz force, which is described by the formula:

F_L = q*v*B

Where:

• F_L - Lorenz force
• q - particle charge
• v - particle speed
• B - magnetic field induction

In this case, the particle moves in a circle, which means that the Lorentz force is directed along the radius of the circle and is the cause of centripetal acceleration. Thus, we can write:

a = (q*v*B)/m

Where m - particle mass. Also, from geometric considerations, we can express the radius of the circle in terms of speed:

r = mv/qB

Substituting the last expression into the formula for centripetal acceleration, we obtain:

a = v²*qB/mv = v*qB/m

Where can you find the speed:

v = a*m/qB

Substituting numerical values, we get:

v = (4*10³*1.6*10^-19*20*10^-3)/(2*10^-2*9.1*10^-31*1.6*10^-19) ≈ 1.75*10⁷ m/s

Thus, the particle's speed is about 17.5 million meters per second.

Product Description: Charged particle that has passed through an accelerating difference

This product represents an interesting problem from the field of physics, which will help deepen knowledge in this science. The problem considers a charged particle that has passed through an accelerating potential difference and began to move in a uniform magnetic field in a circle.

Solving this problem will make it possible to understand how charged particles move in magnetic fields and what forces act on them. Also, this task can be useful for students and schoolchildren when preparing for exams in physics.

The product is designed in a beautiful HTML style, which makes it easy to read and study the problem, as well as easily find the necessary formulas and calculations. By purchasing this digital product, you get access to a complete solution to the problem with a step-by-step description and detailed calculations that will help you understand the processes taking place.

Don't miss the opportunity to expand your knowledge in the field of physics and gain valuable experience in solving problems - purchase the product "Charged Particle Passed by an Accelerating Difference" now!

Product description: "A charged particle that has passed through an accelerating difference"

This product is a problem from the field of physics in which it is required to calculate the speed of a charged particle that has passed through an accelerating potential difference of 4 kV and moving in a uniform magnetic field with an induction of 20 mT around a circle with a radius of 2 cm.

The solution to the problem is based on the use of the formula for centripetal acceleration, as well as the formula for the Lorentz force. The detailed solution contains a brief record of the conditions, the formulas and laws used, the derivation of the calculation formula and the answer.

This product is intended to deepen knowledge in the field of physics and can be useful to students and schoolchildren in preparing for exams. The product is designed in a beautiful HTML style, which makes it easy to read and study the problem, as well as easily find the necessary formulas and calculations.

By purchasing this digital product, you get access to a complete solution to the problem with a step-by-step description and detailed calculations that will help you understand the processes taking place. The solution to the problem can be used both for independent study and for consultation with a teacher.

Don't miss the opportunity to expand your knowledge in the field of physics and gain valuable experience in solving problems - purchase the product "Charged Particle Passed by an Accelerating Difference" now!

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This product describes a physical problem associated with the movement of a charged particle in a magnetic field. A charged particle has passed through an accelerating potential difference of 4 kV and is moving in a uniform magnetic field with an induction of 20 mT around a circle with a radius of 2 cm. It is necessary to determine the speed of the particle.

To solve the problem it is necessary to use the laws of electrodynamics and mechanics. In particular, to find the speed of a particle, you can use a formula that relates the radius of the circle along which a charged particle moves with its speed and magnetic field induction. Also in the calculation it is necessary to take into account the charge of the particle and its mass.

A detailed solution to the problem, including recording the conditions, formulas and laws used in the solution, derivation of the calculation formula and the answer, is presented in a file in image format. If you have any questions about the solution, the author promises to help.

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