(a) Let F₁ = x² 2 and F₂ = x Ŷ + y ŷ + z 2. 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.
(a) Let F₁ = x² 2 and F₂ = x Ŷ + y ŷ + z 2. 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.
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Transcribed Image Text:(a) Let F₁ = x² 2 and F₂ = x x + y ŷ + z 2. 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.
(b) Show that the field F3 = yz î + zx ŷ + xy 2 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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