# Electron with circular trajectory in a magnetic field

• merdeka
In summary, the conversation discusses the calculation of the velocity of a particle using the Lorentz force equation combined with the centripetal force equation for uniform circular motion. The mass of the electron may cancel out in the calculation, but it is unclear without working the problem. The Lorentz force is equal to the centripetal force since it is always perpendicular to the velocity and implies circular motion.
merdeka
Homework Statement
An electron, animated by a speed ##\vec{v}## penetrates a uniform magnetic field ##\vec{B}## . The vectors ##\vec{v}## and ##\vec{B}## are orthogonal, the trajectory of the particle is a circle of radius ##R##.

Calculate the module ##\vec{v}## of the electron's velocity.

me = 9,109 382 15 × 10−31 kg
q = 1,602 176 53 × 10−19 C
B = 1,0 T
R = 1,0 cm
Relevant Equations
##F=q\cdot v\cdot B\cdot\cos(\vec{v},\vec{B})##

I'm not sure how I'm able to calculate the velocity of the particle using the formula without knowing the force exerted on it. Also, I don't understand why the question also provides the mass of the electron.

Just use the Lorentz force equation and combine it with the centripital force equation for uniform circular motion of a mass.

As for the mass of the electron, it may end up cancelling out when you combine those two equations, but I don't know for sure without working the problem.

Please show us those two equations and how you combine them to work toward the solution. Thanks.

I don't understand how the Lorentz force must equal the centrifugal force. I know that their vectors are both orthogonal to ##\vec{v}## and ##\vec{B}##

merdeka said:
I don't understand how the Lorentz force must equal the centrifugal force. I know that their vectors are both orthogonal to ##\vec{v}## and ##\vec{B}##
The Lorentz force IS the centripetal force. There is only one force here.

The key is that the magnetic force is always perpendicular to the velocity. And, if the magnetic force is constant, then this implies circular motion.

berkeman

## 1. What is the concept of an electron with circular trajectory in a magnetic field?

The concept of an electron with circular trajectory in a magnetic field is based on the interaction between the electron's motion and the magnetic field. When an electron moves through a magnetic field, it experiences a force perpendicular to both its velocity and the magnetic field. This force causes the electron to move in a circular path, known as a circular trajectory.

## 2. How does the direction of the magnetic field affect the electron's trajectory?

The direction of the magnetic field determines the direction of the force acting on the electron. If the magnetic field is oriented perpendicular to the electron's velocity, the force will be perpendicular to both, causing the electron to move in a circular trajectory. However, if the magnetic field is parallel to the electron's velocity, there will be no force and the electron will continue in a straight line.

## 3. What is the role of the electron's velocity in its circular trajectory?

The electron's velocity plays a crucial role in its circular trajectory. The force acting on the electron is always perpendicular to its velocity, so the faster the electron is moving, the larger the force will be and the tighter the circular trajectory will be. This is known as the centripetal force.

## 4. Can the radius of the electron's circular trajectory be changed?

Yes, the radius of the electron's circular trajectory can be changed by altering either the strength of the magnetic field or the speed of the electron. A stronger magnetic field will result in a smaller radius, while a higher velocity will result in a larger radius.

## 5. What are some real-world applications of the concept of an electron with circular trajectory in a magnetic field?

This concept has numerous applications in various fields, including particle accelerators, mass spectrometers, and magnetic resonance imaging (MRI) machines. It is also essential in understanding the behavior of charged particles in space, such as electrons in Earth's magnetic field.

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