Quiz _7 F07 - not zero(Ampere’s law-Monday but it is...

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P260 F07 Quiz #7 Name_______________________ A bit more on Potential Theory. We saw for electrostatics that, in the spirit of Helmholtz’s theorem (a vector field is completely specified by its divergence and curl), . 0 0 = × = E and E ε ρ The zero-curl equation is important in that it tells us that the electric field vector can be written as the gradient of a scalar potential function of the position coordinates, V(r). Referring back to quiz #3 you verified the vector identity 0 = × V and thus telling us that we can write V E - = . Now, if we consider our equations for magnetism the curl of B is
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Unformatted text preview: not zero (Ampere’s law-Monday), but it is Gauss’s law that tells us that the divergence of B is zero, . = ⋅ ∇ B Show the vector identity ) ( = × ∇ ⋅ ∇ A and hence conclude that B can be written as the curl of a magnetic vector potential . ), ( A B where r A × ∇ = The physical significance of this magnetic vector potential is not as straightforward to understand as the electric scalar potential, but you will see this again in more advanced E&M courses so it helps to be aware of this concept....
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