What is the Simplified Equation for a Uniform Electric Field?

In summary, a uniform electric field is characterized by a constant magnitude and direction of the electric field at all points in space. It can be created by placing two parallel plates with opposite charges next to each other, and the electric field strength is equal to the voltage difference between the plates divided by the distance between them. The direction of the electric field is always perpendicular to the plates, and a charged particle in a uniform electric field will experience a force in the direction of the field.
  • #1
Goatscholar18
2
0

Homework Statement



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Homework Equations


See Below

The Attempt at a Solution


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Maybe my answer is right but not simplified enough. But if it is I am having trouble seeing the mathematical equivalency. Please help.

Thanks in advance!
 

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  • #2
Most of that is hard to read, but if you just ask about the answer: Factor out 1/4 in the square root and then get it out of the square root.
 
  • #3
Also, I don't think you kept track of the factors of a/2 circled below
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What is a uniform electric field?

A uniform electric field is one in which the magnitude and direction of the electric field are constant at all points in space. This means that the electric field lines are evenly spaced and parallel to each other.

How is a uniform electric field created?

A uniform electric field can be created by placing two parallel plates with opposite charges next to each other. The electric field lines will be directed from the positive plate to the negative plate, creating a uniform field between the plates.

What is the electric field strength in a uniform electric field?

The electric field strength in a uniform electric field is constant and is equal to the voltage difference between the two plates divided by the distance between them. It is typically measured in volts per meter (V/m).

What is the direction of the electric field in a uniform electric field?

The direction of the electric field in a uniform electric field is always perpendicular to the surface of the plates. It is directed from the positive plate to the negative plate.

How does a charged particle behave in a uniform electric field?

A charged particle placed in a uniform electric field will experience a force in the direction of the electric field. The magnitude of the force is equal to the charge of the particle multiplied by the electric field strength. If the particle is positive, it will move in the direction of the electric field, and if it is negative, it will move in the opposite direction.

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