E-B crossed fields parallel plate

[unscientific]

Homework Statement

A parallel plate has p.d. V with one end 0V and the other +V. B-field of strength B has direction along plates. An electron is released from rest at 0V plate. Show that if V is less than e(DB)²/(2m) the electron will not reach the other plate.

Homework Equations

The Attempt at a Solution

At half-way inbetween the plates, the radius must be d/2

R = mv/Bq

d/2 = m*√(2*e*0.5V/m) / (Bq)

I end up with e(DB)²/(4m) instead..

 

[TSny]

At half-way inbetween the plates, the radius must be d/2

Hello.
I don't follow your statement. Could you just as well reason that when the electron is 3/4 of the way across, then the radius must be d/4? If so, would you get the same answer?

I think you're going to need to set up the equations of motion for the x and y components of acceleration.

 

[unscientific]

Hello.
I don't follow your statement. Could you just as well reason that when the electron is 3/4 of the way across, then the radius must be d/4? If so, would you get the same answer?

I think you're going to need to set up the equations of motion for the x and y components of acceleration.

define x as upwards, y into the plate.

ma_x = eV/d

ma_y = qvB

x² + y² = d²

is that right?

 

[TSny]

Let me make sure I understand your choice of directions and signs. Correct me if I'm wrong. You're choosing the electric field in the negative x direction so that the E field accelerates the electron in the positive x direction. The x-axis is oriented perpendicular to the plates.

y-axis is parallel to the plates and B is parallel to the plates but perpendicular to both the x-axis and the y-axis such that when the electron starts moving the B field begins to deflect the electron toward positive y.

But once the electron is deflected some in the y-direction by the B field, the electron will then have a y-component of velocity. So, the magnetic field will then cause some force parallel to the x-axis! So, you need to include a magnetic force term in your equation for a_x.

The electron is going to move along a curved path, so you can't say x²+y² = d² (if d represents the separation of the plates).