What happens when a particle enters an electric and magnetic field at an angle?

[phys02]

Homework Statement

For my physics exam we might need to know what the path of an electron would look like if it entered a magnetic and electric field cause by two parallel plates at an angle. I think it should corkscrew but I'm not sure! Any help?

Also, in only an electric field...would the electron still act as it does when entering the field perpendicular to the E-field, when it enters at an angle?
Thank you!

 

[tiny-tim]

Welcome to PF!

Hi phys02! Welcome to PF!

A uniform electric field has the same effect on a charged particle as a uniform gravitational field … it accelerates it constantly in the fixed direction.

A uniform magnetic field, as you know, makes it spiral.

The two together will be a sort of increasingly floppy spiral.

 

[phys02]

thank you tiny-tim!

just one more thing.
so when if it entered an electric field at an angle it would simply accelerate towards the positive plate still? (fig.1)

And I'm not quite sure how such a spiral would look? Something like (fig.2)? Why?

[my drawings might be wrong i just made a guess at how it would look!)

 

[jasper10]

if BvQ = EQ, then the trajectory would be straight, parallel to both plates.

If one of the forces is greater than the other, the trajectory would be parabolic, and the electrons would go towards that force.

 

[tiny-tim]

so when if it entered an electric field at an angle it would simply accelerate towards the positive plate still? (fig.1)

For zero magnetic field B, yes, it would be parabolic, as in a standard projectile trajectory.

For B non-zero, let's keep B and initial speed v constant, and just increase the electric field E.

For E = 0, the electron will just loop sideways.

As E moves away from 0 (in either direction), the loops will bend in a generally parabolic shape, and the loops will get larger as the speed gets larger.

When E is equal and opposite to Bqv, there will be no loops, and the electron will move in a straight line.

and when E is stronger than that … I'm too confused to figure it out …

 

[jasper10]

so say alpha, on the top diagram, is 30 degrees, and their is no magnetic force. How would you work out the horizontal distance that the particle has traveled along the plate?

 

[tiny-tim]

For B = 0, the "horizontal" velocity would be constant.

If you're asking about the "range", you calculate it exactly the same way as for a projectile (under gravity) at an initial angle of 45º and for the given "height".

 

[jasper10]

so would the horizontal velocity be: ucos30 ?

by the way, I'm in the same class, we both have the same exam tomorrow!

 

[tiny-tim]

so would the horizontal velocity be: ucos30 ?

You mean ucos45º ? Yes.

 

[jasper10]

ok so vertically would these be the kinematic equations...

v = usin45 + at where a = F/m = EQ/m = VQ / dm where V is voltage, d is plate separation, m is mass of particle and q is charge of the particle

this would give: v = usin45 + VQt / dm ?

 

[tiny-tim]

Yes.