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F16 PH333 5.1.1-5.1.3

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Richard Datwyler

on 12 November 2018

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Transcript of F16 PH333 5.1.1-5.1.3

Magnetostatics Lorentz Force Law
5.1.1 Magnetic Fields
5.1.2 Magnetic Forces
5.1.3 Currents

And for our Mechanics lecture today....
Now do the same kind of thing for Electrostatics
Lorentz Force
We make an observation of some physical phenomenon and we want to explain it.
We try to quantify and understand the world around us. Most time experimentation leads theory.
In Electrostatics it was Coulombs law, charges repel or attract other charges
When something unexpected happens we need to ask why.
Force between two wires.
From Electrostatics only how would you describe the following
+
_
What would happen to a test charge then?
+
_
And here?
Can't be electrostatics.
NEW FORCE!!!
Magnetic fields
Compasses, Iron filings, etc show us the direction of a new Field
Forces quantified
This is the Lorentz Force
Currents
Nice steady currents more charges down conductors.
A wire has a linear charge density, and that density must be moving.
We had a current in our wire, quantitatively where is the force?
+
_
Important aside
This last example makes us worry about the work done via magnetic fields
Lets look back to our example of the battery, if we think it is a similar magnetic field causing the current to happen then the work on a small amount of charge in the wire would be.
With dl as
giving
Magnetic forces do no work!!!
so how did the mass get lifted up?
Back to current
From a line density of charge
From a volume density of charge
From a surface density of charge
Being as most things are 3D we should rewrite our magnetic force
Continuity
Our conventional 1D current in a wire, is how much volume current goes through a surface of a wire.
We could scale that up, to every current leaving a closed surface. (divergence theorem)
Which in essence describes a time changing charge distribution.
Solving for this gives a charge continuity equation
Demo
"how do magnetic currents do no work?"
"How do surface and volume current densities work? What do they tell us about the system? I'm having trouble visualizing this."
"Why is current a vector? It goes against everything I thought about how it works. "
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