# Finding the electric field at a point in between 3 electrodes

• kwozz48
In summary, the figure shows three charged metal electrodes with the left electrode as the zero point of electric potential and charges of -q, +Q, and -q on the left, middle, and right electrodes respectively. The distance between the left and middle electrodes is 1 cm and all electrodes have a cross section of 2.0 cm x 2.0 cm. The equations E=Q/(e_0*A) and V=Ed can be used to find the electric field and potential at various points, with the first equation needing to be corrected to E=Q/(2e_0*A). The surface charge density on the inner four surfaces can be used to determine the electric field and potential. However, due to the
kwozz48

## Homework Statement

The figure is an edge view of three charged metal electrodes. Let the left electrode be the zero point of the electric po*tential. Assume that Q=100 nC and q=50 nC.

The left electrode has a charge of -q, the middle electrode has a charge of +Q, and the right electrode has a charge of -q. There is 1 cm in between the left electrode, the middle electrode is 1 cm wide, and there is 1 cm between the middle electrode and the right electrode. All of the electrodes have 2.0 cm x 2.0 cm cross section. I apologize for the lack of a visual, I realize this would make it easier.

a.) What are E at 0.5 cm
b.) What are V at 0.5 cm
c.) What are E at 1.5 cm
d.) What are V at 1.5 cm
e.) What are E at 2.5 cm
f.) What are V at 2.5 cm

E=Q/(e_0*A)
V=Ed

## The Attempt at a Solution

If I have the equations that are supposed to be used correct, then getting parts b, d, and f are very simple. You just plug the answer from parts a, c, and e in correct? I can't figure out how to use the first equation to the get the E field at those points. Any explanation of this problem you can give me would be much appreciated. I need to understand it and be able to work it, not just know the answer. Thanks a lot.

No, your 1st equation is OK. The D field close to a surface charge σ is D = σ.
And D = ε0E and σ = Q/A where Q is the total charge on the surface of area A.

For a dielectric plate the D field close to the plate (but in vacuum) would be σ/2.

Your problem is to determine the surface charge density on all 6 surfaces, then E is immediately available and so as you point out is V.
EDIT: OK, you only need the inner 4 surfaces.

BTW the fact that the plates are only 2 x 2 cm. makes your answers necessarily very approximate since there would be appreciable field fringing taking place.

Last edited:

## 1. How do you calculate the electric field at a point between 3 electrodes?

The electric field at a point between 3 electrodes can be calculated by using the formula: E = k * Q / r^2, where E is the electric field, k is the Coulomb's constant, Q is the charge on each electrode, and r is the distance between the point and the electrodes.

## 2. What units are used to measure the electric field?

The electric field is measured in volts per meter (V/m) or newtons per coulomb (N/C).

## 3. How does the distance between the electrodes affect the electric field?

The electric field is inversely proportional to the square of the distance between the electrodes. This means that as the distance increases, the electric field decreases.

## 4. Can the electric field at a point between 3 electrodes be negative?

Yes, the electric field at a point between 3 electrodes can be negative if the charges on the electrodes are of opposite signs. This means that the direction of the electric field will be towards the electrode with the opposite charge.

## 5. How can the electric field at a point between 3 electrodes be visualized?

The electric field at a point between 3 electrodes can be visualized using electric field lines. These lines represent the direction and strength of the electric field at different points. The closer the lines are together, the stronger the electric field at that point.

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