Field and Wave Electromagnetics 2nd Edition by David Cheng

تمرين 46

For the E of Problem, evaluate E • dl from P 3 (3, 4, -1).to P 4 (4, -3, -1) by converting both E and the positions of P 3 and P 4 into cylindrical coordinates.
Problem:
Given a vector function E = a x y + a y x , evaluate the scalar line integral E • dl from P 1 (2, 1,-1) to P 2 (8, 2, -1)
a) along the parabola x = 2 y 2 ,
b) along the straight line joining the two points.
Is this E a conservative field