Charged particle flying into an electric field

In summary, when a proton enters a magnetic field, it experiences a force given by qvB. The direction of this force is always perpendicular to the velocity of the proton, causing it to move in a circular orbit. The strength of the magnetic field, along with the proton's charge, mass, and velocity, determine the radius of this orbit. The proton also experiences a force along the direction of the magnetic field, resulting in a corkscrew motion. The green lines in the picture represent the magnetic field lines, which are responsible for the proton's movement along their direction.
  • #1
EdTheHead
25
0
If a proton flies into a magnetic field I've seen the trajectory but I'm not sure about the directions of all the forces involved. In this picture
[PLAIN]http://img7.imageshack.us/img7/7065/helicinbfld.jpg
I drew in a red, blue and yellow arrow. I assume the proton is moving in the direction the red arrow which is along the magnetic field lines but I have no idea what direction it was traveling before it entered the magnetic field. Was it traveling in the direction of the yellow arrow before entering the magnetic field then once it entered got stuck in that helicoidal trajectory because of the force exerted by the magnetic field?

Those green lines I assume are the magnetic field lines. If so why is the proton traveling in their direction?
 
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  • #2
The magnetic field induces a force on the proton that is equal to
[tex]\mathbf{F} = q\mathbf{v}\times\mathbf{B}[/tex]
Assume that the B field is along the z direction and we can rotate our coordinate system so that the proton has a velocity with only x and z components. Looking only at the force due to the v_x component, you will find that the magnetic field's force causes the charge to move in a circular orbit. This is because the force changes so that it is always normal to the direction of the velocity in the x-y plane (since B is oriented along the z-axis). The radius of this orbit is dependent upon the charge strength, charge's mass, charge's velocity, and the strength of the magnetic field. The force due to the v_z component is zero as this velocity is directed along the direction of the magnetic field. Thus, the result is that the proton moves in a corkscrew motion.
 

1. What is a charged particle in the context of an electric field?

A charged particle is an object that has an electric charge, either positive or negative. In the context of an electric field, a charged particle is a particle that is affected by the electric field and experiences a force due to its charge.

2. How does a charged particle behave when flying into an electric field?

When a charged particle flies into an electric field, it experiences a force due to the electric field. The direction of the force depends on the charge of the particle and the direction of the electric field. If the particle has a positive charge, it will be pushed in the direction of the electric field. If the particle has a negative charge, it will be pushed in the opposite direction of the electric field.

3. What factors affect the behavior of a charged particle in an electric field?

The behavior of a charged particle in an electric field is affected by several factors, including the charge of the particle, the strength and direction of the electric field, and the mass of the particle. The charge of the particle determines the direction of the force it experiences, while the strength and direction of the electric field determine the magnitude and direction of the force. The mass of the particle affects how quickly it accelerates in response to the force.

4. What is the equation for calculating the force on a charged particle in an electric field?

The force on a charged particle in an electric field can be calculated using the equation F = qE, where F is the force in Newtons, q is the charge of the particle in Coulombs, and E is the strength of the electric field in Newtons per Coulomb.

5. Can a charged particle change its path when flying into an electric field?

Yes, a charged particle can change its path when flying into an electric field. This is because the force on the particle due to the electric field can cause it to accelerate and change direction. The magnitude and direction of the force depend on the charge and mass of the particle, as well as the strength and direction of the electric field.

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