(a) Let Calculate the divergence and curl of F1 and F2. Which one can be written as the...

(a) Let Calculate the divergence and curl of F₁ and F₂. Which one can be written as the gradient of a scalar? Find a scalar potential that does the job. Which one can be written as the curl of a vector? Find a suitable vector potential.

¹⁵In physics, the word field denotes generically any function of position (x, y, z) and time (t). But in electrodynamics two particular fields (E and B) are of such paramount importance as to preempt the term. Thus technically the potentials are also “fields,” but we never call them that.

(b) Show that can be written both as the gradient of a scalar and as the curl of a vector. Find scalar and vector potentials for this function.