# Electron force problem

• jimmy42
In summary, the Lorentz force law states that the net force on a charged particle is equal to the sum of the electric force and the magnetic force acting on the particle. Using this equation, one can determine the direction and magnitude of the electric force needed to create a net force of zero on the particle. This can be done by rearranging the equation and considering the directions of the fields involved.

#### jimmy42

If an electron is pushed up by a magnetic force, the magnetic force acts in the z direction and the electron moves in the x direction, the force is therefore in the y direction. Now if I add an electric force so that the electron carries on in the x direction. Will that electric force need to act in the negative y direction with the same magnitude as the magnetic force?

Thanks.

jimmy42 said:
If an electron is pushed up by a magnetic force, the magnetic force acts in the z direction and the electron moves in the x direction, the force is therefore in the y direction. Now if I add an electric force so that the electron carries on in the x direction. Will that electric force need to act in the negative y direction with the same magnitude as the magnetic force?

Thanks.
That's not quite correct: Let's rewrite it.

"If an electron is acted upon by a magnetic [STRIKE]force[/STRIKE] field, the magnetic [STRIKE]force[/STRIKE] field is in the z direction and the electron moves in the x direction, the force is therefore in the y direction. "

Now if I add an electric force so that the electron carries on in the x direction. Will that electric force need to act in the negative y direction with the same magnitude as the magnetic force?
The answer to the question is YES.

OK thanks. How can I use the Lorentz force law to prove that?

I have done this:

$$E = F - (V x B )/ q$$

Not sure how that equation can tell be the direction. Any help?

The Lorentz force:

$$\vec{F} = q\left[ \vec{E} + \left( \vec{v} \times \vec{B}\right) \right]$$

Everything in the equation is a vector except for the charge, q (which does have a sign though). The "x" is the cross product. The directions of things are determined by the rules of vector manipulation.

In your case you want the net force to be zero, so you can rearrange to solve for E, as you've done. Now, when each of the vectors involved have only a single non-zero component, the expansion of the vector expression into separate component expressions becomes relatively easy (if you want to solve the problem "mechanically"). Otherwise, a little intuition about the directions that the fields must go in order to provide the required force directions on the moving, charged particle will suffice.

I can provide an explanation for the electron force problem described above. Firstly, it is important to understand that forces are vectors, meaning they have both magnitude and direction. In this case, the magnetic force is acting in the z direction and the electron is moving in the x direction, resulting in a force in the y direction. This is due to the right-hand rule, where the direction of the force is perpendicular to both the direction of the electron's motion and the direction of the magnetic field.

Now, if we introduce an electric force in the x direction to keep the electron moving in that direction, we need to consider the net force acting on the electron. Since the magnetic force is acting in the y direction, the electric force must also act in the y direction to balance it out and keep the electron moving in the x direction. However, the magnitude of the electric force does not necessarily need to be the same as the magnetic force. It will depend on the strength of the electric field and the strength of the magnetic field.

In general, the net force on the electron will be the sum of the magnetic and electric forces, taking into account their respective directions. So, the electric force may not necessarily need to act in the negative y direction, as it will depend on the specific scenario and the values of the forces involved. It is important to consider all the forces acting on an object in order to accurately predict its motion.

I hope this explanation helps to clarify the electron force problem. As scientists, we use mathematical models and theories to understand and explain the behavior of particles and forces. It is through careful observation and experimentation that we are able to make predictions and deepen our understanding of the natural world.

## 1. What is the Electron Force Problem?

The Electron Force Problem is a theoretical issue that arises in physics when trying to reconcile the behavior of charged particles, such as electrons, with the fundamental laws of electromagnetism. Specifically, it refers to the difficulty in explaining why electrons do not continuously emit energy as they orbit around an atomic nucleus.

## 2. How is the Electron Force Problem related to the Bohr Model of the Atom?

The Bohr Model of the Atom was one of the first models to successfully explain the behavior of electrons in an atom. However, it also highlighted the Electron Force Problem as it could not fully explain why electrons do not lose energy as they orbit the nucleus, leading to its eventual replacement by more modern models such as the quantum mechanical model.

## 3. What are some proposed solutions to the Electron Force Problem?

There are several proposed solutions to the Electron Force Problem, including the introduction of new fundamental forces or particles, modifications to the laws of electromagnetism, and the incorporation of quantum mechanics. However, none of these solutions has been universally accepted and the problem remains unsolved.

## 4. How does the Electron Force Problem impact our understanding of the universe?

The Electron Force Problem is just one of many unsolved problems in physics that highlights the limitations of our current understanding of the universe. Its resolution could potentially lead to a deeper understanding of the fundamental forces and particles that govern the behavior of matter.

## 5. Are there any real-world implications of the Electron Force Problem?

While the Electron Force Problem may seem like a theoretical issue, its resolution could have significant practical applications. For example, a better understanding of the behavior of electrons could lead to advancements in technology such as more efficient energy storage and transportation systems.