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- #3

berkeman

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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?

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I am not familiar with the lorentz force.

- #5

berkeman

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

I am not familiar with the lorentz force.

[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.

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So only if it has an initial velocity, it won't follow the field lines?

- #7

berkeman

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Yes

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but if you shot it in the direction of a field line, then?

- #10

berkeman

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Now that you've seen the definition of the Lorentz force, what do you think? F=ma, right?but if you shot it in the direction of a field line, then?

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- #13

mfb

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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.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.

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.

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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.So how would it move?

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.

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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.

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yes

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Lets say I release a negative charge from the top of the blue charge.

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I don't understand what you mean by "... from the top of the blue charge..."Lets say I release a negative charge from the top of the blue charge.

View attachment 89785

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 space craft going through the solar system when you dealt with gravity.

Zz.

- #23

mfb

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In general it will not.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.

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.

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