Problem 1 (30 points) - For the following current distributions, sketch the distribution and find

Rai and di(R). (Remember di has a weighting, spatial differential, and direction.)

a) (1 point) Loop carrying current I on the xy plane with radius a centered at the origin.

Give the answers in cylindrical coordinates.

b) (2 points) Loop carrying current I parallel to the xy plane at a height of z=h with radius

a centered at the origin. Give the answers in cylindrical coordinates.

c) (6 points) Loop carrying current I on the xy plane with radius a centered at the point x =

2a, y = 0. Give the answers in Cartesian coordinates. (Hint: use a parametric circle with

0 ≤t<2n.)

d) (6 points) A plate conductor on the xy plane. Current is being injected at a rate of I into

the center of the plate. The current spreads out evenly radially from the origin. (Hint:

remember that the current crossing each concentric ring is also I. Calculate the surface

current density first.) Give the answers in cylindrical coordinates.

e) (6 points) A spherical shell of radius a [m] is centered at the origin. The spherical shell is

evenly charged with ps. []. The shell is rotating around the z-axis with an angular

velocity of wo . Give the answers in spherical coordinates.

f) (3 points) A conducting ring defined in cylindrical coordinates by a ≤p ≤ b,0 ≤ 0 <

2ñ, – ≤ z ≤ with a total current I spread evenly throughout the conductor traveling

counter-clockwise around the ring. Give the answers in cylindrical coordinates.

g) (6 points) The spherical shell from part e) is now a solid sphere with radius a centered at

the origin. The sphere is evenly charged with pvo [] and spinning about the z-axis with

an angualar velocity of wo[ra]. Give the answers in spherical coordinates.