Electron in an Electric Field

Your Name]In summary, the problem involves determining the magnitude of the electric field between two parallel plates based on the path of an electron projected into the field. By using equations for electric force, acceleration, and motion, we can calculate the distance traveled by the electron and the final velocity it reaches before just missing the upper plate. From this, we can solve for the electric field.
  • #1
CEJ__
2
0

Homework Statement


An electron is projected with an initial speed v0 = 1.60 x 10^6 m/s into a uniform field between two parallel plates. Assume that the field between the plates is uniform and directed vertically downward, and that the field outside the plates is zero. 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.

The question gives a diagram which I'll try to reproduce here.

----------- *
| | | | |
e*
| | | | |
-----------

So in this diagram, the top and bottom lines are the plates. e is the electron, and the | are the field lines. The field lines flow from top to bottom. The two *'s are to show the start and end points of the electron--it travels on a parabolic path from the left * to the right *.
The distance between the two plates is 1.00cm, and the length of the plates is 2.00cm.

Homework Equations


The version of the electric field equation that we are using is E = (1/4*pi*k)*q / r^2 where (1/4*pi*k) = 9E9 N*m^2/C^2

The Attempt at a Solution



I thought perhaps we could take the integral of the electric field equation to sum up all the little dr values as the electron travels, but as it starts at .5cm and ends at 0, this gives a rather nasty 1/0 term. There are other parts to the problem, so some of the information might not be useful. Does anyone have any pointers for how to go about this?

-CEJ
 
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  • #2


Dear CEJ,

Thank you for your forum post. To solve this problem, we will need to use the equations for the motion of a charged particle in an electric field.

First, we can use the equation for the electric force on a charged particle, F = qE, to determine the force acting on the electron as it enters the field. Since the electron is negatively charged, the force will be directed upwards, opposite to the direction of the electric field.

Next, we can use the equation for the acceleration of a charged particle, a = F/m, to determine the acceleration of the electron as it travels through the field. Since the electron is moving in a uniform field, the acceleration will also be constant.

We can then use the equations for motion with constant acceleration to determine the path of the electron. Since we know the initial velocity and position of the electron, we can use the equation x = x0 + v0t + (1/2)at^2 to determine the distance the electron travels in the field before it reaches the upper plate.

Finally, we can use the fact that the electron just misses the upper plate to determine the magnitude of the electric field. Since we know the distance the electron traveled and the acceleration it experienced, we can use the equation v^2 = v0^2 + 2ax to determine the final velocity of the electron as it exits the field. From there, we can use the equation F = qE to solve for the electric field.

I hope this helps guide you in solving this problem. Good luck with your calculations!
 

1. What is an electron in an electric field?

An electron in an electric field is a concept in physics that describes the behavior of an electron when exposed to an electric field. The electric field exerts a force on the electron, causing it to accelerate in a certain direction.

2. How does an electric field affect an electron?

An electric field can either attract or repel an electron, depending on the polarity of the field and the charge of the electron. An electron with a negative charge will be attracted to the positive end of an electric field, while an electron with a positive charge will be repelled.

3. What is the relationship between the strength of an electric field and the force on an electron?

The force on an electron in an electric field is directly proportional to the strength of the electric field. This means that the stronger the electric field, the greater the force on the electron.

4. How does the motion of an electron in an electric field differ from its motion in a vacuum?

When an electron is in an electric field, it will experience a force and therefore accelerate in a certain direction. In a vacuum, the electron will continue to move at a constant speed unless acted upon by an external force.

5. Can an electron be in equilibrium in an electric field?

Yes, an electron can be in equilibrium in an electric field if the force exerted by the electric field is balanced by another force, such as the force of gravity. In this case, the electron will not accelerate and will remain at a constant position within the electric field.

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