1. Fields and Waves
Lesson 4.1
MAGNETOSTATICS
Darryl Michael/GE CRD

2. Current sources of magnetic fields ie. currents We will be looking at
description of resistance
We will consider two parameters:
I - Current (in Amps)
J - Current Density (in Amps/unit area)

3. Charge passing through cross-section in time Dt
Current & Current Density
Definition:
Wire with current, I
Charge passing through cross-section in time Dt
Define:
cross-section
In general,
points in direction of current flow

4. Current & Current Density
Example: wire with constant current density
, in cylindrical geometry
Problem 1a - Find I in terms of J0 and invert

5. Problem 1:Current & Current Density

6. Surface Current Density
Surface Current Density Js (in units of A/m)
conductors often have current flowing in thin sheet (eg. High Freq.)
Example: current flow in a wire
Current flow region a
But,
However, define:

7. distance over which current is distributed
Surface Current Density
distance over which current is distributed
Current flow region a
Do Problem 1b
“think of cross-section area and throw out d”

8. Current Density
We now obtain an alternate expression for current density
Wire with current, I
Assume all particles move at same v
In Dt, all particles within Dz=v.Dt will pass through the right face
Cross-section = A
Average velocity
Do problem 1c

9. Resistance , in wire pushed electrons to the right
s, collide with lattice ions
, force (from E-field) driving electrons
, balances
at some
Since
Balance occurs for some value of
for a particular

10. Ohm’s Law Conductivity - units of S/m or 1/ohm-m
varies from 107 to 10-15
Good conductor eg. Cu
Good insulator
, is Fields and Waves version of Ohm’s Law

11. Ohm’s Law
Do problem 2a and 2b…..note for 2b the effective area is an annulus

12. Ohm’s Law Valid if only j and A are constant What if they are not?
Compute V and I separately and form V/I
Example: Disk with Radial Current t V0
Look at wedge
(sketch)
I is the same at the inner and outer part

13. Ohm’s Law - alternative calculation
I is the same at the inner and outer part of disk
Compute potential difference between inner and outer part of disk:
Do problem 2c