What Is the Magnitude of the Electric Field Between Parallel Plates?

[Larissa McNeil]

Homework Statement

An electron is projected with an initial speed v0 = 4.65×106 m/s into the uniform field between the parallel plates in (Figure 1). The direction of the field is vertically downward, and the field is zero except in the space between the two plates. The electron enters the field at a point midway between the plates. If the electron just misses the upper plate as it emerges from the field, find the magnitude of the electric field.
There is a diagram showing the horizontal distance as 2.00cm and the vertical distance as 1.00cm but the electric is situated at half of the vertical distance so 0.5cm.

Homework Equations

kinematics equation: y = vt + 0.5at^2
E=F/q=ma/q[/B]

The Attempt at a Solution

I solved for the horizontal and vertical parts using kinematics.
For horizontal: 0.02=(4.65*10^6)t which equals 4*10^-9
For vertical: (2*0.005)/(4*10^-9)^2 which equals 6.25*10^14
Then I used E=F/q=ma/q:
(9.11*10^-31)(6.25*10^14)/(1.602*10^-19)=3.55*10^3
I've had friends look at my work and they agree with it, but mastering physics keep saying that my answer is wrong. It is due this Sunday and my professor does not like to be emailed. [/B]

 

[haruspex]

Please get into the habit of quoting units everywhere.

For horizontal: 0.02=(4.65*10^6)t which equals 4*10^-9

A little inaccurate.

 

[Larissa McNeil]

My professor showed us how to solve the problem using different numbers. I’m solving it exactly like he did but apparently it’s wrong. My friends who also have to do the homework solved it the way I am and they got it correct. I thought it might be math error but I’ve typed it into the calculator at least ten times.

 

[TSny]

For horizontal: 0.02=(4.65*10^6)t which equals 4*10^-9

As @haruspex noted, you've rounded off too much here. So, your value for t is inaccurate. Later, you square t which just compounds the error. It helps to have your calculator in "scientific notation mode".

 

[haruspex]

As @haruspex noted, you've rounded off too much here. So, your value for t is inaccurate. Later, you square t which just compounds the error. It helps to have your calculator in "scientific notation mode".

To add to that, another good habit to get into is solving problems algebraically as far as you can. It has many benefits.
Normally this means you can get the answer as a single algebraic expression before plugging in any numbers. You can then do all the calculation in one sequence on your calculator, avoiding the rounding errors that result when you type back in numbers from previous steps.