# Magnetic fields, lorentz force

## Homework Statement

an electron accelerated from rest through potential difference V1=0.868 kV enters the gap between two parallel plates having separation d = 21.9 mm and potential difference V2= 91.2 V. The lower plate is at the lower potential. Neglect fringing and assume that the electron's velocity vector is perpendicular to the electric field vector between the plates. In unit-vector notation, what uniform magnetic field allows the electron to travel in a straight line in the gap?

KE = QV
KE = 1/2 mv^2
E= -V/d
E=vB
FE = QE
FB = Qv X B

## The Attempt at a Solution

i know that Q and m are the charge an mass of an electron
to calculate E, i used V2, 91.2V.
I use the equations to solve for v

i know that for the electron to go straight through, the FE=FB,
so i got E = vB
then i solved for B

and since B is a cross product of vectors on an xy plane, It HAS to only have a direction perpendicular to them on the z axis

in the end, i get 0i + 0j + 2.38e-4k T
but it's wrong...
I have a feeling that this is supposed to be one of the easier questions too :S

collinsmark
Homework Helper
Gold Member
[...] and since B is a cross product of vectors on an xy plane, It HAS to only have a direction perpendicular to them on the z axis
Almost!, but not quite. The electric force is already along the z-axis (the problem statement mentioned something about a lower plate, implying there is an upper plate, implying that one plate is above the other). Which means to counteract the electric force, the magnetic force you are looking for must also be along the z-axis!

So the magnetic field vector must be perpendicular to the force vector and also the velocity vector. But since the force vector is on the z axis, the magnetic field vector must be along some other axis.
The magnitude of your magnetic field vector looks good to me. . (Just work on the direction. )