Motion of charge in electric and magnetic fields

In summary, a proton is accelerated from a rest position into a uniform electric field and magnetic field that are perpindicular to each other, as shown. The proton passes through the parralel plates without being deflected, at a constant velocity. When the proton leaves the plates, it only experiences a magnetic force. The magnitude of the electric field is 1.2 x 10^4 n/c and the magnetic field is 0.20T.
  • #1
krbs
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3

Homework Statement


A proton is accelerated from a rest position into a uniform electric field and magnetic field that are perpindicular to each other, as shown, The proton passes through the parralel plates without being deflected, at a constant velocity. When the proton leaves the plates, it only experiences a magnetic force. The magnitude of the electric field is 1.2 x 10^4 n/c and the magnetic field is 0.20T.

IMG_3457.JPG


a) Find the speed of the proton.
b) Find the radius of the path of the proton as it leaves the plates.

Homework Equations


FM = qvB
FE = Eq
Fc = (mv^2)/r

The Attempt at a Solution



a) Fnet = FM + FE
0 = FM - FE
FM = FE
qvB = Eq
v = E/B
= (1.2 x 10^4 N/C) / (0.20 T)
= 6.0 x 10^4 m/s

b) FM = FC
qvB = mv^2/r
qB = mv/r
r = mv/qB
= (1.67e-27 kg)(6.0e4 m/s)/(1.60e-19 C)(0.20T)
= 3.1 x 10^-3 m

I'm not certain how to think about this situation since the velocity associated with magnetic force is perpendicular to the force.
 
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  • #2
krbs said:
I'm not certain how to think about this situation since the velocity associated with magnetic force is perpendicular to the force.
Why is that a problem?
 
  • #3
It's not a problem so much as a source of uncertainty/confusion for me. I'm used to working with net force in one dimension at a time.

The electric force between the plates is pushing down on the proton but not causing it to move from it's horizontal path. I assume that's because there's an equal and opposite magnetic force pointing up? And the proton is moving sideways because of the magnetic force? So there's no horizontal force. It is moving at a constant velocity, so no acceleration.
 
  • #4
krbs said:
And the proton is moving sideways because of the magnetic force?
Not sure what you mean by that. Sideways with respect to its initial motion or sideways as viewed in the image? The magnetic force will be vertical. By 'moving' do you mean accelerating?
Other than that, what you wrote looks right.
 
  • #5
Oh, when it's between the plates it's moving at a constant velocity rightwards, in the diagram, perpendicular to the magnetic force, because of the magnetic force?
 
  • #6
krbs said:
Oh, when it's between the plates it's moving at a constant velocity rightwards, in the diagram, perpendicular to the magnetic force, because of the magnetic force?
Depends what you mean by "because of the magnetic force". It moves at constant velocity because there is no net force, and that is because the electric and magnetic forces cancel (which you used in your calculation).
 
  • #7
Okay, the proton was accelerated outside the fields and already had that speed upon entering them. The magnetic force is not actually giving it speed. Absent the electric field, the uniform magnetic field would cause the proton to curve off into uniform circular motion, but instead the electric force pushes back down on it so it stays in a straight line.

Do my steps look about right?
 
  • #8
krbs said:
Okay, the proton was accelerated outside the fields and already had that speed upon entering them. The magnetic force is not actually giving it speed. Absent the electric field, the uniform magnetic field would cause the proton to curve off into uniform circular motion, but instead the electric force pushes back down on it so it stays in a straight line.

Do my steps look about right?
Yes.
 
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Likes krbs
  • #9
Alright, thanks for your help
 

Related to Motion of charge in electric and magnetic fields

1. What is the difference between electric and magnetic fields?

Electric fields are created by stationary charges, while magnetic fields are created by moving charges. Electric fields exert forces on other charges, while magnetic fields only exert forces on moving charges.

2. How does a charge move in an electric field?

A charge will experience a force in the direction of the electric field. If the charge is positive, it will move in the direction of the electric field. If the charge is negative, it will move in the opposite direction.

3. What is the role of a magnetic field in the motion of a charged particle?

A magnetic field exerts a force on a moving charge, causing it to move in a circular path perpendicular to the direction of the magnetic field. This is known as the Lorentz force.

4. How do electric and magnetic fields interact with each other?

When a charged particle moves in a magnetic field, it creates an electric field. Similarly, when a charged particle moves in an electric field, it creates a magnetic field. This interaction is known as electromagnetic induction.

5. How do electric and magnetic fields affect the speed of a charged particle?

Electric fields do not affect the speed of a charged particle, but they can change its direction of motion. Magnetic fields, on the other hand, can change both the direction and speed of a charged particle, as they can do work on the particle by exerting a force.

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