Dipole Fields: Definition & Examples

Instructor: Laura Foist

Laura has a Masters of Science in Food Science and Human Nutrition and has taught college Science.

In this lesson, we will learn what a dipole field is, and how to calculate the electric field strength at different points in the field. We will also look at some example calculations.

The Dipole Field

Imagine that you and your friend tied sticks to either side of a rock. Your friend starts pushing on one stick, while on the other side you start pulling on the other stick. Eventually, that rock is going to move, in your direction. The force that the rock is feeling is the combined force of you and your friend.

Dipole fields, or an electric field between two charges of the same but opposite strength, work in a similar way to the poles on the rock. Since positive charges have a field going out of them (pushing) and negative charges have a field going towards them (pulling) they create a current going from the positive charge to the negative charge. Charges are coming and going to all directions on both charges, and with a single point charge, these forces will be straight lines. But these lines curve towards the other charges when we have a dipole.

Let's look at the positive charge, the charges would start going straight out from the positive charge, but would begin to curve inwards, towards the negative charge. We end up with a field of curved lines:


When two charges with equal but opposite charges are placed near each other, a field with curved lines is created.
Dipole field curved lines


The X-axis in the Dipole Field

We can draw an x and y-axes in the dipole field, with the y-axis coming exactly halfway between the two charges and the x-axis going straight from one charge to the other. At any point along these axes, we can calculate the strength of the dipole field.

The dipole field can have an x and y-axis, and we can calculate the field strength at any point along those axes
Dipole field with axes and points

Let's look back at our rock example, if your friend is the positive charge (pushing) and you are the negative charge (pulling) then the purple circle can be the rock, in-between both of you.

We know that the 'rock' will move towards the negative charge. We can calculate the force felt by that 'rock' by using Coulomb's law, where the electric strength equals Coulomb's constants times the two charges, divided by the distance between the two charges squared. The force from each charge can be calculated and added together to find the total force felt by that point (or the 'rock').

The equation for Coulombs law
Equation for coulombs law

Example Equation

Let's look at a dipole field with the two charges having a strength of 4 microcoulombs. The two charges are 5 cm away from each other. What would be the electric field strength at a point 2 cm away from the positive charge (3 cm away from the negative charge)? We already know it will move towards the negative charge, and that both forces are pushing it in that direction, so now we just need to calculate the strength.

E=?

q= 4uC = 4x10 -6 C

k= 9.0 x 10 9 N*m 2/C 2

r(positive)= 2 cm = 0.02 m

r(negative) = 3 cm = 0.03 m

Calculating the electric field for the positive charge
Calculate electric field for positive

Calculating the electric field for the negative charge
Calculate electric field for negative charge

E = 1.2x106 + 1.8x106 = 3.0x106 N

The Y-axis in the Dipole Field

Determining the force felt along the y-axis is a little bit more complicated. Let's say that you now tied sticks at an angle on the rock. Your friend is still pushing on the stick and you are still pulling on the stick, but in what direction will the rock move?


We can calculate the electric field strength along the y-axis
Point on y-axis


In order to determine this, we need to draw the vectors of each charge. Let's start with the positive charge, the y-vector is going upwards while the x-vector is going to the right:


Vectors on positive charge
Vectors on positive charge


Now, let's draw the vectors for the negative charge, the y-vector is going downwards while the x-vector is going to the right:


Vectors on negative charge
Vectors on negative charge


Now we can combine the vectors:


Combined vectors
Combining vectors


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