Magnetic Field, Potential, Velocity

[fredrick08]

Homework Statement

An electron travels with speed 1.0 x 107
m/s between the two parallel charged
plates shown in the adjacent figure. The
plates are separated by 1.0 cm and are
charged by a 200 V battery. What magnetic
field strength and direction will allow the
electron to pass between the plates without
being deflected?

Homework Equations

B=($$\mu$$/4$$\pi$$)(qvsin$$\theta$$/r$$^{2}$$)

The Attempt at a Solution

well I am pretty sure that F=0N, and the the direction the field has to be in the same direction of the velocity, so sin(theta)=0... but i have no idea how find the field strength, anyone have any ideas?

 

[fredrick08]

wat can i do with this Voltage... i need a current don't i?... i can't find the right formulas, and getting really frustrated.. argh

 

[Defennder]

The question referred to a picture. It may require a picture or at least an accurate description before we can help. Is the electron traveling in a direction parallel to the plates?

 

[fredrick08]

yes sorry... the electron is traveling parallel through the parallel plates.. i see if i can upload pic

 

[Defennder]

Well if that's the case, no picture is required. Just think in terms of how much force is needed to counter-balance the force exerted on the particle by the E-field. Then use the Lorentz force equation to find the magnetic flux density needed.

 

[fredrick08]

oh i don't know if we are meant to do it like that, because we havnt done flux or lorentz...

 

[fredrick08]

 

[Defennder]

Well, "magnetic flux density" is another word for "magnetic field strength" and "Lorentz force" is a more general term for "force on charged particle due to B-field".

 

[fredrick08]

oh ok so F=(E+v X B)... i don't understand because doesn't f have to equal 0, for the electron to pass through undisturbed, as soon as there is a force the electron is going to change direction? unless its opposing the velocity, which would make it slow down?

 

[fredrick08]

thus E=V/s=200/.01=2000N/C but how do i find B?

 

[Defennder]

oh ok so F=(E+v X B)... i don't understand because doesn't f have to equal 0, for the electron to pass through undisturbed, as soon as there is a force the electron is going to change direction? unless its opposing the velocity, which would make it slow down?

You're missing out q here. F has to be zero in order for the electron to pass undeflected. Note that the force exerted by the E-field and that by the B-field is perpendicular to its velocity, and hence does not affect its speed in that direction.

thus E=V/s=200/.01=2000N/C but how do i find B?

Use the equation you stated earlier. Although another similar approach would be to separate the two equations: F=qE and F=Bqv and this two are acting in opposite directions, so you equate them and solve for B. Note that you have to indicate the direction in which the B-field is applied.

 

[fredrick08]

yes sorry i missed q... so qE=Bqv =>E=Bv=>B=E/v=2000/1x10^7=2x10^-4T in the direction of the velocity?

 

[Defennder]

Check your value for E-field. And note note that magnetic force will always act in a direction perpendicular to both the velocity and direction of the B field. Use the right-hand rule to get the direction.

 

[fredrick08]

ya its 20000 not 2000... oh ok yes i remember now... duh... lol so the direction of B will be out of the page? since the E travels + to -...

 

[Defennder]

Remember this is an electron, not a positive charged particle.

 

[fredrick08]

na I am confused... what does this mean... won't the electron want to move towards the positive charged plate??

 

[fredrick08]

oh for an electron its the exact opposite, so use left hand, so its going into the page? but is my maths correct, does 2mT sound right?

 

[fredrick08]

no wait before i was using my left hand ad it was saying out... my right says in, thereofre it must be out of the page? please help I am really confused

 

[Defennder]

No I meant to say that when you apply the F=qv X B vector equation you must note that the resulting direction using the right-hand rule holds for a positive charge. The negative charge goes in the opposite direction.

 

[Defennder]

Don't use your left hand. Your right hand would do, just reverse the direction.

 

[fredrick08]

yes so if my right hand says the direction is into the page for a +ve charge it is out the page for a -ve charge ie, an electron?

 

[Defennder]

EDIT: Ok, you're right on this. You can visualise the +ve charged particle as moving from the right to the left. By the way, don't switch it around twice; either consider an equivalent positive charged particle or just reverse the direction at the end of your hand-twisting. Don't do both.

Just consider a positive charge from left to right (same as the electron). Assume the B-field passes into the page. Use the right hand rule and reverse the direction at the end. Is the result the direction you want? If not, assume instead the B-field passes out of the page and do the same.