# Help With Dipoles: Finding Electric Field E(x,y)

• paulyspike
In summary, a dipole is a pair of equal and opposite charges separated by a small distance and is a fundamental concept in electromagnetism. The electric field of a dipole can be calculated using the formula E = kq/r^3 and can also be found by taking the gradient of the electric potential function. The direction of the electric field due to a dipole depends on the location of the point in space, and the electric field can cancel out at certain points, known as neutral points. The strength of the electric field decreases with distance from the dipole, following an inverse-cube law.
paulyspike
Help With Dipoles!

I need some help on a question..how to set it up and solve it. Here is the question:

Find the general expression for the electric field E(x,y) for a dipole charge +/- Q and length d oriented along the y-axis and symmetric about the x-axis.

Thank you.

Tell us what you've done so far, so that we can know from where to help you.

Sure, I'd be happy to help with your question on finding the electric field for a dipole charge. First, let's start with the definition of an electric field: it is the force per unit charge experienced by a test charge placed at a certain point in space. In this case, we are looking for the electric field at any point (x,y) in space due to a dipole charge.

To set up this problem, we can use the principle of superposition, which states that the total electric field at a point is the sum of the electric fields due to each individual charge. In this case, we have two charges (+Q and -Q) separated by a distance d along the y-axis. We can also use the fact that the electric field due to a point charge is given by the equation E = kQ/r^2, where k is the Coulomb's constant, Q is the charge, and r is the distance from the charge to the point where we want to find the electric field.

So, at a point (x,y), the electric field due to the positive charge will be E1 = kQ/(x^2 + (y-d)^2) and the electric field due to the negative charge will be E2 = -kQ/(x^2 + (y+d)^2). Notice that we have taken the direction into account by adding a negative sign for the negative charge.

Now, to find the total electric field at (x,y), we simply add these two electric fields together: E(x,y) = E1 + E2 = kQ/(x^2 + (y-d)^2) - kQ/(x^2 + (y+d)^2).

This is the general expression for the electric field at any point (x,y) due to a dipole charge. You can simplify it further by using the fact that d is the distance between the two charges, so (y-d) and (y+d) can be replaced by just y, giving us: E(x,y) = 2kdQ/(x^2 + y^2).

I hope this helps you set up and solve your problem. Remember to always double check your units and use the correct values for k and Q. Let me know if you have any further questions or need clarification. Good luck!

## 1. What is a dipole?

A dipole is a pair of equal and opposite charges that are separated by a small distance. It is a fundamental concept in electromagnetism and can be found in many real-world applications, such as in antennas and molecules.

## 2. How do I calculate the electric field of a dipole?

The electric field of a dipole can be calculated using the formula E = kq/r^3, where k is the Coulomb's constant, q is the magnitude of the charge, and r is the distance from the dipole. Additionally, the electric field can be found by taking the gradient of the electric potential function.

## 3. What is the direction of the electric field due to a dipole?

The direction of the electric field due to a dipole depends on the location of the point in space. At points along the axis of the dipole, the electric field is directed from the positive to the negative charge. At points perpendicular to the axis, the electric field is directed either towards or away from the dipole, depending on the orientation of the charges.

## 4. Can the electric field of a dipole cancel out?

Yes, the electric field of a dipole can cancel out at certain points in space. This is known as a neutral point and occurs when the distance from the dipole is equal to the separation between the charges. At this point, the electric field due to the positive and negative charges will be equal in magnitude but opposite in direction, resulting in a net electric field of zero.

## 5. How does the strength of the electric field change with distance from a dipole?

The strength of the electric field due to a dipole decreases as the distance from the dipole increases. This relationship follows an inverse-cube law, meaning that the electric field strength decreases by a factor of r^3 as the distance r increases. This is because the electric field is spread out over a larger area as the distance from the dipole increases, resulting in a weaker field.

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