## Introduction

Hello it's a me again Drifter Programming!

After covering Electric fields we can now continue on with **Physics **and more specifically **Electromagnetism **to talk about **Electric Dipoles**, that **create an unique electric field**.

So, without further do, let's get straight into it!

## Electric dipole

Suppose we have **2 point charges q1 and q2** that have the** same amount** (meter) **of charge**, but of **opposite sign**. This means that q1 for example has a charge +q, while q2 has a charge -q. This exact **combination **of charges is called an **Electric dipole**! Let's also say that the **distance **between those charges is **d**.

Now there are two **questions **that need to be answered:

- What kind of forces (F) and torques (τ) are applied to a dipole when it's inside of another electric field?
- What kind of electric field does it create/generate?

Let's answer each one by it's own starting of with the first one.

## Electric dipole torque and potential

Let's put a dipole inside of an uniform electric field E.

The forces **F+ and F-** of course have the **same value**/meter **qE**, but also have an **opposite direction** and so **cancel each other out**!

We can see that:

The total force applied to an electric dipole inside of an uniform electric field is zero.

But, those forces are not going to the same direction which means that **the total torque is not zero**! [Torque is something that we will cover later on in Classical mechanics, but just so that you understand it now think of it as "something" that makes objects rotate.]

Anyway, supposing the **angle **between the uniform electric field E and the axis of the dipole is φ and by also including the **concept of electric dipole torque as*** p = ql* (in C*m) we have that the

**torque**is:

Or by using an more general vector form we could say:

**τ = p x E**

Because of this cross product we have that:

- the torque is maximum when p and E are vertical across (φ = π/2)
- the torque is zero when p and E are parallel (φ = 0 or π)

The torque always tries to **rotate the dipole so that it gets parallel to the uniform electric field**!

By doing so the torque does a **Work **(also something that we will cover later in Classical mechanics):

Because W = U1 - U2 (also something that we will cover later on) we have that the** electric potential** is:

**U(φ) = -PEcosφ**

or

**U = -p*E**

in vector form

And so:

- the potential energy is minimum (maximum negative) when φ = 0
- the potential energy is maximum when φ = π
- the potential energy is zero when φ = π/2

When the electric field is **non-uniform **then the dipole will also have a force applied to it, which means that it will move to some direction. So, **an object with zero sum of charge, but dipole torque (q*l) will have a force applied to it when inside of an non-uniform electric field**!

In exercises of dipoles we of course will use those equations, but because it's more Classical mechanics then Electromagnetism I think that I will not get into many examples :)

## Electric dipole field

Lastly, let's also get into how such a dipole electric field looks like!

The following is an electric dipole field:

As mentioned in my previous post we make the** electric field lines go from positive to negative charges**. But, here you can also see that because the charges are equal we also have an equal distribution of the field.

At each point of this electric field E the **total electric field **is the vector sum of the fields E+ and E- created by the charges q+ and q- individually.

But, how do we calculate this field?

Well, let's get into a simple example where we calculate the **electric field of an dipole that is on-top of the y-axis at a point P at (0, y)**

Supposing that the point P is at y and that the center of the dipole is at O (0, 0) having the positive "pole" be at d/2 and negative "pole" at -d/2 we have:

Because y is much larger then d we can approximately get the simpler equation:

Of course if the point P was not at some axis (y or x) then the mathematical equations would become more complex, but I guess that you got an idea of how we calculate them :)

Well, a lot of this stuff was not covered yet in Classical mechanics and so I suppose that someone will understand this post better if he/she already knows the concepts of work, energy and potential. But, don't worry you can get back to it after I cover it in Classical mechanics if you have problems at the moment :)

## Previous posts about Physics

**Intro**

Physics Introduction -> what is physics?, Models, Measuring

Vector Math and Operations -> Vector mathematics and operations (actually mathematical analysis, but I don't got into that before-hand :P)

**Classical Mechanics**

Velocity and acceleration in a rectlinear motion -> velocity, accelaration and averages of those

Rectlinear motion with constant accelaration and free falling -> const accelaration motion and free fall

Rectlinear motion with variable acceleration and velocity relativity -> integrations to calculate pos and velocity, relative velocity

Rectlinear motion exercises -> examples and tasks in rectlinear motion

Position, velocity and acceleration vectors in a plane motion -> position, velocity and accelaration in plane motion

Projectile motion as a plane motion -> missile/bullet motion as a plane motion

Smooth Circular motion -> smooth circular motion theory

Plane motion exercises -> examples and tasks in plane motions

Force and Newton's first law -> force, 1st law

Mass and Newton's second law -> mass, 2nd law

Newton's 3rd law and mass vs weight -> mass vs weight, 3rd law, friction

Applying Newton's Laws -> free-body diagram, point equilibrium and 2nd law applications

Contact forces and friction -> contact force, friction

Dynamics of Circular motion -> circular motion dynamics, applications

Object equilibrium and 2nd law application examples -> examples of object equilibrium and 2nd law applications

Contact force and friction examples -> exercises in force and friction

Circular dynamic and vertical circle motion examples -> exercises in circular dynamics

Advanced Newton law examples -> advanced (more difficult) exercises

**Electromagnetism**

Getting into Electromagnetism -> electromagnetim, electric charge, conductors, insulators, quantization

Coulomb's law with examples -> Coulomb's law, superposition principle, Coulomb constant, how to solve problems, examples

Electric fields and field lines -> Electric fields, Solving problems around Electric fields and field lines

And this is actually it for today and I hope that you learned something!

Next time we will get into Exercises/Examples for Electric charge, fields and dipoles :)

Bye!