## Find scalar and vector potentials for this function.

- Let \(F_1=x^2ẑ\) and \(F_2=x\:x̂+y\:ŷ+z\:ẑ\). Calculate the divergence and curl of \(F_1\) and \(F_2\). 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.

In physics, the word field denotes generically any function of position \(\left(x,\:y,\:z\right)\) and time \((t)\). But in electrodynamics two particular fields \(\left(E\:and\:B\right)\) are of such paramount importance as to preempt the term. Thus technically the potentials are also “fields,” but we never call them that. - Show that \(F_3=yz\:x̂+zx\:ŷ+xy\:ẑ\) 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.

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Electromagnetic Theory
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