How to Determine Proton Movement in Electric and Magnetic Fields?

[Astronuc]

The problem is one of a velocity selector, in which the force imposed by the electric field is equal and opposite the force imposed by the magnetic field on the moving proton.

Doc Al gave a good link to the Lorentz force on hyperphysics.


Both the electric and magnetic fields are vector fields.


No the proton moves up in a magnetic field which goes into the paper/screen. So what direction is the resultant force based on F = q (v x B)? Bold used to indicate vector.

Then to balance that force, the electric force must be in the opposite direction. In addition to opposite directions, the balancing forces must have equal magnitudes in order to add to zero.

 

[Doc Al]

so the electric field is in a positive directoion?

\vec{F}_e = \vec{E} q

For a positive charge, the electric force is in the same direction as the electric field.

I urge you to study the two sites I provided. Ben Crowell has kindly seen fit to make his textbooks available for free. Take advantage of this!

 

[physicsbhelp]

wait astronuc, what do you mean.

doc al and the other person said that the magnetic force is in the -x direction and the electric force is in the +x direction.

and you said that:
"the electric field is equal and opposite the force imposed by the magnetic field on the moving proton."

so since the magnetic field is into the page (-z) then the opposite would be +z ??

 

[physicsbhelp]

this is still for part a) btw.

 

[physicsbhelp]

okay so i am trying to understand this electric field stufff by the websites. and this is what i get "The electric field from a positive charge points away from the charge; the electric field from a negative charge points toward the charge. " and since we are talking about a proton, it is a positive charge. so the electric filed will point away from the charge.


so is the electirc filed in the positive x direction? since its pointing away?

 

[Astronuc]

so since the magnetic field is into the page (-z) then the opposite would be +z ??

Careful. Do not confuse magnetic field with magnetic force.

The magnetic force on a moving charge is perpendicular to the plane formed by the velocity and magnetic field vectors by virtue of v x B.

Please follow Doc Al's guidance.

 

[physicsbhelp]

wait, how am i confusing magnetic force and field?

and i really don't get the perpendicular part.

is doc al back yet?

 

[Doc Al]

wait astronuc, what do you mean.

doc al and the other person said that the magnetic force is in the -x direction and the electric force is in the +x direction.

and you said that:
"the electric field is equal and opposite the force imposed by the magnetic field on the moving proton."

so since the magnetic field is into the page (-z) then the opposite would be +z ??

Read carefully. Equal and opposite the magnetic force, not the magnetic field. (Astro and I are saying the same thing, of course.)

okay so i am trying to understand this electric field stufff by the websites. and this is what i get "The electric field from a positive charge points away from the charge; the electric field from a negative charge points toward the charge. " and since we are talking about a proton, it is a positive charge. so the electric filed will point away from the charge.


so is the electirc filed in the positive x direction? since its pointing away?

Those sites are talking about the field of a point charge--but that's not related to this problem. You want to understand the force on a charge due to an external field. See my previous post (#32).

 

[Astronuc]

The electric field (a vector field) imposes a force (a vector) which is parallel with the field.

A magnetic field (a vector field) imposes a force which is perpendicular to the magnetic field. The magnetic force is proportional cross (vector) product of the velocity vector and magnetic field vector.

One is trying to find the magnitude and direction of the electric field such that the force on the proton is equal in magnitude, but opposite in direction, to the force imposed by the magnetic field (\vec{B}).

 

[physicsbhelp]

i am not trying to find the magnitutde of the elctric field.



and now i understand you doc al.

but where do i find ben crowell's txt books.

i don't have that much time on my hands. its true.

 

[physicsbhelp]

so if the electric field is not in the +z or +x direction, it must be in the +y direction right?

 

[Astronuc]

so if the electric field is not in the +z or +x direction, it must be in the +y direction right?

Go back to post #9, where you are correct on the direction of the magnetic force. The electric force must be in the opposite direction in order to be able to cancel the magnetic force.

 

[physicsbhelp]

i know that Astronuc, i know that the electric Force is in the +x but i am looking for the electic field.

 

[physicsbhelp]

wiat astronuc said that electirc filed is parallel to magnetic field?
so is it also in the -z diretion??

 

[Doc Al]

i am not trying to find the magnitutde of the elctric field.

But you do need the direction of the electric field.

but where do i find ben crowell's txt books.

I gave his link in post #26.

so if the electric field is not in the +z or +x direction, it must be in the +y direction right?

Who said that it's not in one of those directions? Answer each of these questions:

Which way does the magnetic force point?

Which way must the electric force point to balance the magnetic force?

So which way must the electric field point to produce such a force? (See post #32.)

 

[physicsbhelp]

Who said that it's not in one of those directions? Answer each of these questions:

Which way does the magnetic force point?

Which way must the electric force point to balance the magnetic force?

So which way must the electric field point to produce such a force? (See post #32.)

1) -x
2) +x
3) +x

 

[physicsbhelp]

3) ?

 

[Doc Al]

1) -x
2) +x
3) +x

Exactly!

 

[Astronuc]

1) -x
2) +x
3) +x

Correct.

If the velocity vector direction is +y, and the magnetic field is +z (into the page), then the cross (vector) product must be -x, by the right hand convention. Therefore the electric field vector must point in the opposite (+x) direction, in order to impose a force on a 'positive' charge in the +x direction.

 

[physicsbhelp]

THANKS!


now for part b) ;)

 

[physicsbhelp]

now i have to : Determine the speed of the proton while in the box if it continues to move vertically upward. Express your answer in terms of the fields and the given quantities.

to find velocity do i use the formula Fm=qv*B

 

[physicsbhelp]

but how can i express myh anwer in terms of the fields when i am not given anything about charge.
do i somehow need to incorporate the proton.

or should i use a different formula.

 

[Doc Al]

You need to solve for the speed in terms of both fields. Set up an equation for the net force on the charge in terms of the fields. (What's the net force on the charge?)

 

[Astronuc]

Fm=Fe

qvB=qE??

Correct. Note that the charge cancels. Charge by the way is a scalar quantity.

Now solve for v.

 

[physicsbhelp]

thanks

 

[physicsbhelp]

this is for part c) On the figure above, sketch the path of the proton after it leaves the box.

 

[physicsbhelp]

which one is it? i drew all three of them, i just don't know which way I am supposed to draw it.

 

[Astronuc]

What is the trajectory of charge moving in a constant magnetic field?

Hint - http://hyperphysics.phy-astr.gsu.edu/Hbase/magnetic/maspec.html

 

[physicsbhelp]

too complicated words? i am not sure what you mean, i looked at the hint.
wait why can't you tell me because i drew those three image.s

 

[Astronuc]

too complicated words? i am not sure what you mean, i looked at the hint.
wait why can't you tell me because i drew those three image.s

trajectory is the path. What path does a charged particle of constant speed take in a uniform magnetic field?