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 Fields||Generated by mass||Field strength is represented by g|
|Electric Fields||Generated by electric charge (+ or -)||Field strength is represented by E|
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 materials||Ex: Iron, cobalt, nickel are magnetic due to their chemical structures|
Force acts from North to South
|By moving electric charges||Ex: 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 pole||Around 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:
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.
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:
|force on a current-carrying conductor is maximum when the wire is perpendicular to the magnetic field||force 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 field||force 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:|
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 experiences||F = 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 wire||The force calculated will be the SAME for both wires!|
|This works regardless of the direction of the current in either wire||If 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:
- 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