# Current / Magnetism Questions: Proton near magnetic field of moving electrons

In summary, a problem involving electrons and positive particles moving at 1x10^8 m/s in opposite directions, with a proton moving on top of the electron beam at the same speed, is being observed by a person standing and a person running at the same speed. The current flows to the right. In the reference frame of the person standing, the magnetic force on the proton can be calculated using F=qvB. The forces of attraction and repulsion between the electrons and the proton cancel out. In the reference frame of the running person, the magnetic force on the proton is replaced by the force of the electric field. The beam moving with the runner appears stationary, while the other beam appears to move almost twice as fast. The

## Homework Statement

Ok guys, this problem has a few steps to it, and id appreciate any help I can get.

Ok, so beam of electrons moving left, positive particles with same but opposite charge moving right, both moving at 1x10^8 m/s. Then there is a proton moving left on top of the beam nearby AT ALSO 1x10^8 m/s. A person standing nearby is observing, and so is a guy running ALSO 1x10^8 m/s nearby.

Questions:
1) Direction of current?
2) Force on the proton as seen by the person standing, and the person running seperatly.
3) Velocity/direction of the two beams from the running persons point of view?
4) What current will the man running measure and in which direction?

## Homework Equations

1) none
2) F=qvBsin(theta) (or in this case just F=qvB since the direction of the proton is perpendicular to the magnetic field..?)
3) none
4) ?

## The Attempt at a Solution

1) Current flows is opposite of current flow, so therefore in this case current flows to the right. Is this correct?

2) Person standing still: There is a magnetic field flowing out of the screen from the view we have, if the current is indeed traveling to the right. Therefore, I simply use the equation F=qvB to solve. Is this true, or would I need to factor in the fact that the electrons are also drawing the particle towards them?

Person running: since he is moving at the same speed and direction as the proton, it will seem to him that it is not moving.

3) The beam moving in the same direction will seem as though it doesn't move, but the beam moving in the opposite direction will seem to move twice as fast.

4) will he measure no current? since he is moving as fast as the electrons?Thanks for any help guys! I appreciate it.

Last edited:
1) I assume you meant to say that current flows in the opposite direction from electron flow? Anyway, to the right is correct.

2) In the reference frame of the person standing, yes, use F = qvB. Think about this: if the electrons are attracting the proton towards them, why would the positive particles (in the current) not also be repelling the lone proton away from them? How do the strengths of these two effects compare?

In the reference frame of the running person: yes, he sees it as not moving and therefore sees no magnetic force. But he sees another force acting on the proton in place of the magnetic force. Can you identify it?

3) The beam moving along with the runner (that is, the electrons) will seem to him like it's not moving, true. The other beam will seem like it's moving almost twice as fast. (Why not exactly twice as fast?)

4) Aren't you forgetting the beam of positive particles?

Have you studied relativity? I am wondering because the speeds involved are (1/3)c. If one were not to consider relativistic effects, why pick this particular speed for charge distributions and observer?

Diazona-

You brought up some amazing points! Thank you so much for your help.

For number 2, for the person running, you are referring to the force of the electric field, am I correct?

And one other question, what direction would the electron seem to be traveling from the point of the running person?

## 1. What is the relationship between a proton and a magnetic field created by moving electrons?

The relationship between a proton and a magnetic field created by moving electrons is that the proton will experience a force if it is placed near the magnetic field. This force is known as the Lorentz force and is perpendicular to both the direction of the magnetic field and the direction of motion of the electrons.

## 2. How does the strength of the magnetic field affect the force experienced by a proton?

The strength of the magnetic field directly affects the force experienced by a proton. The stronger the magnetic field, the greater the force acting on the proton will be. This is because the force is directly proportional to the strength of the magnetic field.

## 3. How does the direction of the magnetic field affect the force experienced by a proton?

The direction of the magnetic field also plays a role in the force experienced by a proton. If the direction of the magnetic field is parallel to the direction of motion of the electrons, the proton will not experience any force. However, if the direction of the magnetic field is perpendicular to the direction of motion of the electrons, the proton will experience a maximum force.

## 4. What is the difference between a magnetic field created by a moving charge and a magnetic field created by a permanent magnet?

The main difference between a magnetic field created by a moving charge (such as electrons) and a magnetic field created by a permanent magnet is that the latter is a static field, while the former is a dynamic field. This means that the strength and direction of the magnetic field created by a moving charge can change, whereas the magnetic field of a permanent magnet remains constant.

## 5. How does the motion of the electrons affect the strength of the magnetic field?

The motion of the electrons has a direct impact on the strength of the magnetic field. The stronger and faster the motion of the electrons, the stronger the magnetic field will be. This is because the magnetic field is created by the movement of charged particles, and the stronger the movement, the greater the resulting magnetic field will be.

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