# PHY C22: Magnetic Fields

A new field!

• Magnetic Fields
• Magnetic Field Lines
• Force on a current-carrying conductor in a magnetic field
• F = BIL sin θ
• Force between parallel current-carrying conductors

What is a magnetic field?
A region of space where a force is exerted on a magnetic pole OR a moving charge.

We know that every field is generated & affected by some property:

So,

How are magnetic fields generated?
Unlike the fields we have seen before, there are 2 ways a magnetic field can be created:

Although it seems strange that there are 2 unrelated reasons for a single force to appear, they are actually similar at the quantum level. I won’t get into that in this post, but you can check out these links to investigate why:

Just like other fields, magnetic fields describe how forces act on magnetic poles/moving charges.

We should be familiar with the basic properties of magnetic force:

• It effects 2 possible poles (North & South)
• Like poles repel
• Unlike poles attract

## The strength of a magnetic field is represented by B.

This value is more accurately known as MAGNETIC FLUX DENSITY, which I will cover in the next post.

We can represent magnetic fields via Magnetic Field Lines.

Characteristics of field lines:

Remember that these diagrams only show a 2D CROSS SECTION of the actual field, which is 3D!

Falstad.com has a beautiful applet for simulating 3D magnetic fields, check this out:

Let’s take a closer look at the

# Magnetic Force (AKA Motor Effect)

Simple enough?
However, remember that this force also effects MOVING CHARGES, in a different way.

This effect has many names, from the Laplace Force to the Magnetic Force.
Here, I will refer to it as the Motor Effect (but check your syllabus to see what they prefer!).

Where does the Motor Effect come from?
A common explanation is the superposition of magnetic fields: The original uploader was Theresa knott at English Wikibooks., CC BY-SA 2.5 https://creativecommons.org/licenses/by-sa/2.5, via Wikimedia Commons

How can we calculate the force generated?

## F = BIL sin θ

The direction of this force can be determined using Fleming’s Left Hand Rule*:

*There are different variants of this rule, use the one you’re most comfortable with!

For those who are into maths, this means that the force F is the cross product of the electric force vector & the magnetic force vector:

This implies a few things:

So far we’ve looked at the:

• force between 2 magnets
• force between a magnet & a current-carrying conductor

…but how about the:

# Force between 2 parallel conductors

Once again, we can use the principal of superposition to explain this: