What is the Path and Speed of a Proton in a Magnetic Field?

[aldaris565]

Homework Statement

A proton travles with a velocity 8x10^5 m/s E=10^6 V/m and B= 1.5 T. Draw the path of the proton and what is speed of the proton when it comes out?

Here an image:

Homework Equations

The Attempt at a Solution

 

[JaredJames]

As per PF rules, you need to show your own attempt before we can help you.

Please don't double post. Use this one, not the one in General Physics.

 

[aldaris565]

Yeah ok, I'm newbie in this forum... that's what i did :

[PLAIN]http://img222.imageshack.us/img222/3104/imagengh.jpg


But i don't know what else to do.. please help me =)

 

[JaredJames]

OK, so you have the method, but where's your working?

 

[aldaris565]

Well just replace with the values given...I'm stuck i don't know if that's correct or not... I decided do it with all variables and then replace them...

I guess i sould integrate the speed getting the position (x,y) but I'm not sure if that's correct...

I need help.. I HAVE to resolve this problem...

I need ideas you don't have to resolve all the problem.. just give me ideas!

 

[berkeman]

Well just replace with the values given...I'm stuck i don't know if that's correct or not... I decided do it with all variables and then replace them...

I guess i sould integrate the speed getting the position (x,y) but I'm not sure if that's correct...

I need help.. I HAVE to resolve this problem...

I need ideas you don't have to resolve all the problem.. just give me ideas!

What is the shape of the path of a charged particle in a uniform magnetic field?

You correctly list the Lorentz force as the force that is acting on the proton in the magnetic field (there is no E field, right?). What does that Lorentz force do to the path of the proton? Draw the path, and plug in the numbers for the force. The force acts over a finite distance of the proton's trajectory -- what is the resulting trajectory when the proton leaves the B-field region?

 

[aldaris565]

What is the shape of the path of a charged particle in a uniform magnetic field?

You correctly list the Lorentz force as the force that is acting on the proton in the magnetic field (there is no E field, right?). What does that Lorentz force do to the path of the proton? Draw the path, and plug in the numbers for the force. The force acts over a finite distance of the proton's trajectory -- what is the resulting trajectory when the proton leaves the B-field region?

But in the problem exist an E field... the trajectory doesn't have to be exact... i guess it's a Uniform Circular Movement.

If i'd do:

First for t=0 -> x=0 y=0.05
Then:
Finding t=? for x=0.3 y=0.05

That would be correct¿? then i replace that value of t in the formula of the speed... would i get the final speed (when it comes out) ??

 

[berkeman]

But in the problem exist an E field... the trajectory doesn't have to be exact... i guess it's a Uniform Circular Movement.

If i'd do:

First for t=0 -> x=0 y=0.05
Then:
Finding t=? for x=0.3 y=0.05

That would be correct¿? then i replace that value of t in the formula of the speed... would i get the final speed (when it comes out) ??

Ah yes, I missed that there is an E field too. So you have to use the full Lorentz force in the region between the plates, and account for the deflecting forces from the E and B fields.

If it were only the B-field, then yes, the particle would trace a circular path. Given the B-field direction shown, would the proton be deflected up or down by that B-field?

But you do need to add in the contribution of the E field as well. Which way will the E-field try to deflect the proton?

Since both the E and B fields are constant in the region between the plates, you should be able to just add their contributions. However, the bending path will make the proton stay between the plates a little longer than if it traveled in a straight line, so there may be an integration involved...

 

[berkeman]

Maybe try solving separately for the E-field case and the B-field case, to see about what you can expect for the combined case, before doing any complicated integrals...

 

[aldaris565]

The integrals are no so complicated... but in another forum someone told me that the proton never leaves and the path i guess it's not a straight line, because qE is diferent that q(vxB) [q(vxB) and qE are in opossite directions but they aren't equals to eliminate them...]

 

[berkeman]

The integrals are no so complicated... but in another forum someone told me that the proton never leaves and the path i guess it's not a straight line, because qE is diferent that q(vxB) [q(vxB) and qE are in opossite directions but they aren't equals to eliminate them...]

What radius do you get for a B-field only version of this problem?