# How to derive kinetic energy equation for charged particles

• Proz3m0
In summary, the conversation is about a new formula derived for charged particles in a magnetic field. The formula is derived from the kinetic energy equation and takes into account the Lorentz force exerted on a charged particle moving under a magnetic field. The original poster is seeking help in understanding the derivation of this new formula.
Proz3m0
I know there are some threads discussing about the Lorentz force equation but this is something different I came across and I couldn't find anyway to derive that formula.

To be specific I'm talking about a charged particles in a magnetic field, where F=vqB and everything that is moving has kinetic energy, later on I was shown that kinetic energy 1/2mv2 = q2B2R2 / 2m

Can anyone show me how that new formula is derived?

Welcome in Physics Forum!
For threads posted under the Homework section, the post is recommended to follow the given template, in addition the OP should also show some initial effort in solving his/her own problem. For instance the template asks the OP to write down any related formula, besides F=qvB what other equation do you have for a charged particle moving under a magnetic field? Hint: consider the nature of the magnetic Lorentz force.

Last edited:
Imagine a happy charged particle wizzing around when, all of a sudden, it enters a magnetic field, and here when the lorentz force come in F = q (v x B) and the field exert a force on the particle that is orthogonal to it's velocity one thing you can predict is that the particle will rotate (will prove it if you want,but not now) and when an object rotate there is some force forcing it to stay in orbit that is the lorentz force (a centripital force), Good luck !

## 1. What is kinetic energy for charged particles?

Kinetic energy for charged particles is the energy that a charged particle possesses due to its motion. It is a form of energy that is associated with the movement of charged particles in a field.

## 2. How is kinetic energy for charged particles derived?

Kinetic energy for charged particles is derived using the equation K = ½mv², where K is the kinetic energy, m is the mass of the charged particle, and v is the velocity of the particle.

## 3. What are the units of kinetic energy for charged particles?

The units of kinetic energy for charged particles are Joules (J) in the SI system or electron volts (eV) in the CGS system.

## 4. Can kinetic energy for charged particles be negative?

Yes, kinetic energy for charged particles can be negative if the particle is moving in the opposite direction of the applied force or if its velocity decreases over time.

## 5. How does kinetic energy for charged particles relate to other forms of energy?

Kinetic energy for charged particles can be converted into other forms of energy, such as electrical potential energy or heat, depending on the type of field the particle is moving in. It is also a component of the total energy of a charged particle, which includes its potential energy and rest mass energy.

Replies
4
Views
1K
Replies
14
Views
1K
• Introductory Physics Homework Help
Replies
5
Views
262
• Introductory Physics Homework Help
Replies
5
Views
267
• Introductory Physics Homework Help
Replies
21
Views
2K
• Classical Physics
Replies
3
Views
764
• Special and General Relativity
Replies
4
Views
1K
• Electromagnetism
Replies
8
Views
1K
• Mechanics
Replies
11
Views
1K
• Introductory Physics Homework Help
Replies
4
Views
840