Use an expansion in rectangular coordinates to show that the curl of the gradient of any scalar field G is identically equal to zero.

2. A filamentary conductor on the z axis carries a current of 16 A in the az direction, a conducting shell at ρ = 6 carries a total current of 12 A in the −az direction, and another shell at ρ = 10 carries a total current of 4 A in the −az direction. (a) Find H for 0