Dot product: A.B = Ax Bx + Ay By + Az Bz = A B cos q
Cross product: |AxB| = A B sin q =
L = r x mvExamples of vector products
Gradient of a scalar function = slope in each direction
Divergence of vector = dot product = what flows out
Curl of vector = cross product = circulationDifferential operator “del”
Ex: If v = E, then div E = charge; if v = B, then curl B = current.
Position vector = location of a point with respect to the origin.
Separation vector: from SOURCE (e.g. a charge at position r’) TO POINT of interest (e.g. the place where you want to find the field, at r).
What surface charge density does it take to make Earth’s field of 100V/m? (RE=6.4 x 106 m)
2.12 (p.75) Find (and sketch) the electric field E(r) inside a uniformly charged sphere of charge density r.
2.21 (p.82) Find the potential V(r) inside and outside this sphere with total radius R and total charge q. Use infinity as your reference point. Compute the gradient of V in each region, and check that it yields the correct field. Sketch V(r).