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:

Gravitational FieldsGenerated by massField strength is represented by g
Electric FieldsGenerated by electric charge (+ or -)Field strength is represented by E

So,

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

By permanently magnetic materialsEx: Iron, cobalt, nickel are magnetic due to their chemical structures

Force acts from North to South
By moving electric chargesEx: Moving electrons, protons, α-particles, or current in a wire

Force acts according to the right hand grip rule

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:

By convention, arrows show the direction of forces acting on a North poleAround permanent magnetic poles, lines always start at N & end at S:



Around moving charges, lines always obey the right hand grip rule:
They are always smooth curves which never touch or cross 
Density of lines indicate strength of field

Closer lines = stronger field
 
Neutral points exist where there are no field lines
(forces cancel each other out, so there is no net force in that region)

The area between the 2 magnets has no field lines, so it is a neutral point.

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)

If I place a small magnet in a large permanent magnetic field like this:


It would experience a force like this:

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

If I place a STATIONARY positive test charge in a large permanent magnetic field like this:


It would experience NO FORCE.
If I place a positive test charge which is MOVING INTO THE PAGE in a large permanent magnetic field like this:


It would experience a FORCE like this:
The same goes for a current-carrying conductor placed like so:

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:

If a permanent magnetic field & a magnetic field due to a wire look like this: 
The superposition of the 2 fields looks like this:
As there are more field lines on 1 side of the conductor, a force is generated from this side to the side with less field lines.
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*:

Jfmelero, CC BY-SA 4.0 https://creativecommons.org/licenses/by-sa/4.0, via Wikimedia Commons

*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:

F = IL x B
Read more on cross products at Maths Is Fun.

This implies a few things:

force on a current-carrying conductor is maximum when the wire is perpendicular to the magnetic fieldforce on a moving charge is maximum when the direction of motion is perpendicular to the magnetic field
force on a current-carrying conductor is 0 when the wire is parallel to the magnetic fieldforce on a moving charge is 0 when the direction of motion is parallel to the magnetic field

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:

When both currents are in the same direction:
When the 2 currents are in opposite directions:
Images from S-Cool

But we can also use the Motor Effect to CALCULATE the force between 2 wires!

Here’s our example setup: 
We can treat 1 wire as a permanent magnet generating field lines into the page

There is a formula to calculate the magnetic field strength due to a wire, but it is not required for A-Levels. Read more about it here.
We can treat the other wire as a current-carrying conductor in a permanent magnetic field & calculate the force it experiencesF = BIL sin θ

Since θ = 90°,
F = BIL
We can do this in any order & get the same answer!
This works regardless of the magnitude of current in either wireThe force calculated will be the SAME for both wires!
This works regardless of the direction of the current in either wireIf both currents flow in the same direction, the wires will be pushed closer together:


If the 2 currents flow in opposite directions, the wires will be pushed apart:
MikeRun, CC BY-SA 4.0 https://creativecommons.org/licenses/by-sa/4.0, via Wikimedia Commons

REMEMBER:

  • BOTH forces are EQUAL in magnitude & OPPOSITE in direction (Newton’s 3rd Law)
  • the force ‘between’ the 2 wires is NOT the sum of the 2 forces, it is EQUAL to the 2 forces

3 thoughts on “PHY C22: Magnetic Fields

  1. Pingback: PHY C22: Magnetic Flux Density – ProDuckThieves

  2. Pingback: PHY C22: Charged Particles in Magnetic Fields – ProDuckThieves

  3. Pingback: PHY C23: Lenz’s Law & further explanations on EM Induction – ProDuckThieves

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