Charge Particle Trajectory: How to Find It

In summary: like a mass... is shot out at an angle with respect to the horizontal, it will follow a curve path, depending on the angle it is shot at.
  • #1
UMath1
361
9
My textbook said that field lines do not always represent the trajectory of a charged particle in a field. How would you find the trajectory then?
 
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  • #2
What points? Let's say you had a field created by one positive charge and one negative charge. If a negative test charge would not flow along the field line from positive to negative, how would it flow if it started at the positive end?
 
  • #3
UMath1 said:
My textbook said that field lines do not always represent the trajectory of a charged particle in a field. How would you find the trajectory then?

What field? Electric or Magnetic or both? A static field or a changing field? What it the initial trajectory of the charged particle with respect to the field(s)? Are you familiar with the Lorentz Force? Can you show us that equation?
 
  • #4
Electrostatic field. The negatively charged particle is just let go from the positive end.

I am not familiar with the lorentz force.
 
  • #5
UMath1 said:
Electrostatic field. The negatively charged particle is just let go from the positive end.

I am not familiar with the lorentz force.

The Lorentz Force is the vector force acting on a charged particle that is moving in magnetic and/or Electric fields:

[tex]F = qE + q(vxB)[/tex]

If you just release a charged particle from rest, yes it will follow the E-field lines, because that's the direction of the Lorentz force when there is no B field.
 
  • #6
So only if it has an initial velocity, it won't follow the field lines?
 
  • #7
If you shot the charged particle into a region of E-filed that was perpendicular to the motion, then the particle would follow a curved path, correct?
 
  • #8
Yes
 
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  • #9
but if you shot it in the direction of a field line, then?
 
  • #10
UMath1 said:
but if you shot it in the direction of a field line, then?

Now that you've seen the definition of the Lorentz force, what do you think? F=ma, right?
 
  • #11
Right, but the direction of the force constantly varies if the field line is curved as it often is between positive and negative charges. It should move tangent to the field line initially. But I am not sure if after it moves in that direction, it will still be acted on by the same field line.
 
  • #12
To find the equation of motion just write down F=ma for the system and solve. Alternatively you can use the Lagrangian to determine the equation of motion.
 
  • #13
berkeman said:
If you just release a charged particle from rest, yes it will follow the E-field lines, because that's the direction of the Lorentz force when there is no B field.
It will do that "in the first moment", but it won't do that in general, even if it starts at rest. If the field lines are curved, the particle won't follow them.
UMath1 said:
Right, but the direction of the force constantly varies if the field line is curved as it often is between positive and negative charges. It should move tangent to the field line initially. But I am not sure if after it moves in that direction, it will still be acted on by the same field line.
Your doubt is right here. To follow a curved line it would need an acceleration component orthogonal to the field line, but that does not exist by definition of the field line.

A magnetic field can change the trajectory, but in general it won't make particles follow any field lines.
 
  • #14
mfb said:
It will do that "in the first moment", but it won't do that in general, even if it starts at rest. If the field lines are curved, the particle won't follow them.

Yes, sorry. In his initial example, I thought he was talking about straight E-field lines.
 
  • #15
mfb said:
Your doubt is right here. To follow a curved line it would need an acceleration component orthogonal to the field line, but that does not exist by definition of the field line.

So how would it move?
 
  • #16
UMath1 said:
So how would it move?

Have you solved a projectile motion in gravity? I find it hard to believe that you are doing charged particle in electric field and not have already tackled a projectile motion. If you have, then you really should go back and look at it, because, believe it or not, you already know how to solve this.

If you look at the projectile motion, the "field lines" are always pointing down, because this is the field lines for gravity. If you simple let go of a mass, how does it move? Does it move in the same direction of the "field lines"?

But what if you shoot the mass out at some angle with respect to the horizontal? How does it move then?

Look at the electrostatic problem and see why it is no different.

Zz.
 
  • #17
But the field lines for gravity point in a constant direction. When you have a positive and negative charge, the field lines take a curved path. If a charge carrier is released in the direction of one of these curved lines, a force tangent to the curved line will act on it causing acceleration tangent to the line. But after that I don't see where the force will act on it.
 
  • #18
UMath1 said:
But the field lines for gravity point in a constant direction. When you have a positive and negative charge, the field lines take a curved path. If a charge carrier is released in the direction of one of these curved lines, a force tangent to the curved line will act on it causing acceleration tangent to the line. But after that I don't see where the force will act on it.

So let me get this clear. If I give you an electrostatic field that is constant everywhere, and looks just like a gravity field, you can solve this easily, correct?

Zz.
 
  • #19
yes
 
  • #20
UMath1 said:
yes

Fine.

Now tell me exactly the field lines that you have.

Zz.
 
  • #21
Lets say I release a negative charge from the top of the blue charge.
250px-VFPt_dipole_electric.svg.png
 
  • #22
UMath1 said:
Lets say I release a negative charge from the top of the blue charge.
View attachment 89785

I don't understand what you mean by "... from the top of the blue charge..."

Regardless of that, when you have a field such as this, for an electron, the trajectory will closely follow the field lines when you release the charge from rest. However, the larger the mass, the longer the path, and the more accurate you want your answer, the more it will deviate from these field lines. If you want an accurate modeling of such path, you will have to solve the equation of motion for such a system, and it may not be an analytical solution (i.e. you might only be able to solve it numerically).

It is why you were never asked to solve for the path of a spacecraft going through the solar system when you dealt with gravity.

Zz.
 
  • #23
ZapperZ said:
Regardless of that, when you have a field such as this, for an electron, the trajectory will closely follow the field lines when you release the charge from rest.
In general it will not.
Using the position description of post #21 and some rough estimate on the positions, I would expect our test mass to be unbound. It won't follow the field lines - it will not even stay in the picture, but escape nearly vertically, crossing field lines nearly orthogonally on its way out.

To make the charged particle follow field lines, you would need some resistance (like residual gas for collisions).

The mass is not relevant here, it just changes the timescale, but not the result.
 

1. What is a charge particle trajectory?

A charge particle trajectory is the path that a charged particle takes as it moves through an electric or magnetic field. This can be calculated using equations from electromagnetism and the principles of particle motion.

2. How do you find the charge particle trajectory?

To find the charge particle trajectory, you will need to know the initial conditions of the particle, such as its velocity and position, as well as the strength and direction of the electric or magnetic field it is moving through. You can then use equations such as the Lorentz force law and Newton's laws of motion to calculate the trajectory.

3. What factors affect the charge particle trajectory?

The charge particle trajectory is affected by several factors, including the strength and direction of the electric or magnetic field, the mass and charge of the particle, and the initial conditions of the particle. Other factors such as external forces, collisions with other particles, and relativistic effects may also play a role.

4. Can the charge particle trajectory be changed?

Yes, the charge particle trajectory can be changed by altering the strength or direction of the electric or magnetic field it is moving through. This can be done by manipulating the equipment or by changing the properties of the field itself.

5. Why is it important to calculate the charge particle trajectory?

Calculating the charge particle trajectory is important for understanding the behavior of charged particles in various fields. This has practical applications in fields such as particle physics, electronics, and space science. It also helps us to better understand the fundamental principles of electromagnetism and particle motion.

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