Chapter 5, Problem 29P

(a)

To determine

Check whether the current density $J=2x^{3}y{a}_x+4x^2{z}^2{a}_y-6x^{2}yz{a}_z$ is possible for static (time-independent) fields.

(b)

To determine

Check whether the current density $J=xy{a}_x+y\left(z+1\right)a_y+2y{a}_z$ is possible for static (time-independent) fields.

(c)

To determine

Check whether the current density $J=\frac{z^2}{\rho }{a}_{\rho }+z\cos \varphi a_z$ is possible for static (time-independent) fields.

(d)

To determine

Check whether the current density $J=\frac{\sin \theta }{r^2}{a}_r$ is possible for static (time-independent) fields.