• Dealing with all the different “r's”
• Understanding r -r'
• Primes not as derivatives

• Electric potential
• Magnetic Vector Potential
• Densities that are not M/V (including surface and linear densities and charge and currrent densities)

• Integration as chopping and adding
• Curvilinear coordinate systems
• Gradient
• Divergence
• Curl
• Matrix operations

Examples

• Finding current from Q and T of a spinning ring
• Choosing coordinate systems that take advantage of symmetry of a ring
• Starting with the general formula for volume current density and reducing it to a formula for linear current density
• Determining that several variables can be held constant during integration (e.g. z, R, etc in ring problem)
• Understanding that an arbitrary point can be used to find an equation for “all space”

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1) Choosing a coordinate system (G4,1:21)

2) Dealing with all the different “r's” :

a) R as radius;

b) r as position vector of “voltmeter”;

c) r' as position vector to dQ on ring;

d) r - r' as the vector between dQ and “voltmeter”; (G4,1:22)

e) script r as | r - r'|; (G4,1:25)

f) r as in V( r), simply refering to a variable that varies across space.

3) dr vs d(theta) (G4, 1:26-1:30)

4) The problem of “solving for potential in all space” and realizing that solving for a single point does this.

5) Determining what is held constrant during integration

6) The relation between V = kQ/r and the integral form of the equation (G4,1:22-1:24)

7) Determining where the charge is. There is confusion about whether there is a piece of charge at the location at which the potential is measured (the location of the “voltmeter”) (G4,1:28)

8) Whether to integrate in one, two, or three dimensions (one for a linear density, two for the area of the plane in which the ring is located and three for all space). Included in this is recognizing a circle as an inherently one-dimensional object

9) The nature of electric potential as different from electric field (e.g. the potential for the ring is not zero at the origin and there are no cancelling vectors)

10) Needing to put r - r' into rectangular coordinates