ECE390 Homework #1
A. Determine the gradient of the scalar field (in cylindrical coordinates):
V (r , φ , z ) = r z cos(2φ )
B. Determine the divergence of the vector field (in Cartesian coordinates):

P ( x, y, z ) = x 2 yzxˆ + xzzˆ
C. Determine the curl of the vector field (in spherical coordinates):

1
ˆ + R sin(θ ) cos(φ )θˆ + cos(φ )φˆ
P ( R, θ , φ ) = 2 cos(θ )R
R
D. The flow of water in a pipe is faster in the middle than near the outside.
For a 2 cm diameter pipe, given that the velocity of the water as a function of
distance from the center of the pipe is:
v(r ) = (1 − r 2 / cm 2 )1.48m / s
Determine the total flow in the pipe in liters/second.