Gauss's law states that ∫ S B → ⋅ d S → = 0. But law of induction states that ξ = − d ϕ d t , where ϕ = ∫ S B → ⋅ d S → So if Gauss's law was to be correct there should be no induction at all, because then ϕ would be zero through every loop.

Question

Gauss&#039;s law states that       ∫    S              B      →        ⋅  d            S      →        =  0. But law of induction states that   ξ  =  −            d      ϕ              d      t      , where   ϕ  =      ∫    S              B      →        ⋅  d            S      →      So if Gauss&#039;s law was to be correct there should be no induction at all, because then ϕ would be zero through every loop.

odvucimo1pp17 · Accepted Answer

The definition of magnetic flux is  Φ  =      ∫    S    d            A      →        ⋅            B      →        ,where the integral is not over a closed surface in general. Gauss&#039; Law requires that the integral is over a closed surface, and so there is no contradiction.In particular, look at any basic discussion of Faraday&#039;s Law. They always look at simple loops or coils of wire. There are clearly not closed surfaces, and so the definition of flux can&#039;t involve a closed surface in these cases. Without a closed surface it&#039;s easy to think of cases where the field gives nonzero flux.

measgachyx5q9 · Accepted Answer

Gauss&#039;s law states that       ∫    S              B      →        ⋅  d            S      →        =  0 for a closed surface, while the induction law relates the flux through an open surface to the electromotive force (  ξ) in the circuit formed by its border

Gauss's law states that ∫ S </msub> <mrow class="MJX-TeXAtom-O

Answered question

Answer & Explanation

New Questions in Electromagnetism