How to find electric field given points of electric potentia

In summary, the problem is to find the electric potential and field at any point, given the coordinates of two points with known potential values of 0V and 1V. This assumes that there are no other charges in the universe. It is uncertain if there is a solution to Maxwell's equations that meets these conditions.
  • #1
Erwin Derek
I have what at first seems like a very simple problem, yet I have no clue how to solve it.

There is 1 point defined to have 0V, and another point has exactly 1V. Assume there is nothing else in the universe.

https://i.imgur.com/iv9oL5j.png

How do I find the electric potential and field at any other point, assuming all I know is the coordinates of these two points?

Would this require delta function / laplace equation or something?
 
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  • #2
Erwin Derek said:
Assume there is nothing else in the universe.
Do you mean to assume that there are no charges anywhere in the universe? I am not sure that there is a solution to Maxwell's equations that fits your requirements here
 

1. How do I find the electric field at a specific point using the electric potential?

The electric field at a specific point can be found by taking the negative gradient of the electric potential at that point. This means taking the partial derivative of the electric potential with respect to both the x and y coordinates of the point and multiplying them by -1. The resulting vector will give you the magnitude and direction of the electric field at that point.

2. Can the electric field be calculated at any point if the electric potential is known?

Yes, as long as the electric potential is known at all points in the surrounding area, the electric field can be calculated at any point using the method described in the previous answer. This is because the electric field is directly related to the electric potential through the gradient.

3. How do I determine the direction of the electric field using the electric potential?

The direction of the electric field can be determined by looking at the sign of the partial derivatives of the electric potential at the point in question. If the partial derivative with respect to the x coordinate is positive, the electric field will point in the positive x direction, and if it is negative, the electric field will point in the negative x direction. The same applies for the y coordinate.

4. What units are used to measure electric potential and electric field?

Electric potential is typically measured in volts (V) while electric field is measured in volts per meter (V/m). However, they can also be expressed in other units such as joules per coulomb (J/C) for electric potential and newtons per coulomb (N/C) for electric field.

5. How does the distance between two points affect the electric field when calculating it using the electric potential?

The electric field is inversely proportional to the distance between two points. This means that as the distance between two points decreases, the electric field will increase and vice versa. This relationship is described by Coulomb's law, which states that the magnitude of the electric field between two points is equal to the electric potential difference divided by the distance between the two points.

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