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A vector field that has no curl can be written as the gradient of a potential
function. As a consequence we can describe the electrostatic field as such a gradient. A vector field that, like B, has vanishing divergence, can be written as the curl of a vector potential in a similar way. we can define the vector potential A so that In the case of static currents where there is no time dependence we set We can solve this equation in all of space with the boundary condition that A go to 0 at infinity just as we solved for V. The result, exactly like that for V in the last chapter is In the time dependent case we define the vector potential A by These definitions do not determine A and V completely. Given any scalar
field f, we can add Exercise 29.4 Find the equations satisfied by A and V implied by Maxwell's
Equations (including sources |
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