## Find scalar and vector potentials for this function.

1. 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.
2. 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 1 Answer Anonymous(s) Post