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?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?
The Lorentz Force is the vector force acting on a charged particle that is moving in magnetic and/or Electric fields:Electrostatic field. The negatively charged particle is just let go from the positive end.
I am not familiar with the lorentz force.
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.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.
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?
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?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.
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.
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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.