What Magnetic Field Keeps an Electron Moving Horizontally?

[nick227]

Homework Statement

A 10keV electron moving horizontally enters a region of space in which there is directed downward an electric field of magnitude 100V/cm. (a) what are the magnitude and direction of the smallest magnetic field that will allow the electron to continue to move horizontally? Ignore the gravitational force. (b) If the electric field is produced by a capacitor whose plates are 2.50m apart, describe the trajectory of the electron if the electric field is turned off when the electron enters the field (i.e. just the magnetic field is left on.)

Homework Equations

E/B = V/Bd

The Attempt at a Solution

if I'm trying to find B,i can find the voltage by converting the 10keV and E is given also, but what is d?

 

[muppet]

I don't recognise that equation immediately... and maybe I'm just tired at ten to three in the morning but it looks to me like B should cancel from both sides, rendering it useless! What does it mean, and where does it come from?

If I were you, I'd want the expression for the force exerted on a charged, moving particle by electric and magnetic fields. What's that?

 

[nick227]

I don't recognise that equation immediately... and maybe I'm just tired at ten to three in the morning but it looks to me like B should cancel from both sides, rendering it useless! What does it mean, and where does it come from?

If I were you, I'd want the expression for the force exerted on a charged, moving particle by electric and magnetic fields. What's that?

are you thinking of the lorentz law? f=qE+qv X B? though, coulomb's law also comes into mind.

i was looking through my book and found this equation:

e/m_e = V(theta)/(B²ld)

this was in the chapter where the question came from, in the section where the question came from...

but how does this relate to the electric field?

 

[muppet]

I've no idea! Yes, I was thinking of the lorentz force. If it was a classical mechanics problem, and you had an equation which gave you all of the forces acting on the object, what would you do if you wanted the object to carry on its constant motion in a straight line?

 

[nick227]

wouldn't the magnetic be the same as the electric field, just opposite in direction. because if you want the electron to have no deflection, the B-field and E-field have to be the same in different direction (i think). so using that theory (its probably wrong), the magnetic field is 100 and it is the direction is directed upwards.

 

[muppet]

You're on the right lines, but not quite. You need the forces to balance (How would you represent this in an equation?) but it doesn't quite follow that the fields are opposite, because the force exerted by a magnetic field doesn't act in the direction of the field (Just to confuse you )