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Assuming the system follows Maxwell's equations, what must both fields satisfy such that

##∇⋅(\frac{∂B}{∂t})=0## ?

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- Thread starter tade
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In summary, both the scalar field ρ(x,y,z,t) (charge density) and the vector field J(x,y,z,t) (current density) must satisfy Maxwell's equations in order for the equation ∇⋅(∂B/∂t)=0 to hold. This leads to the conclusion that Gauss' Law for Magnetic Flux is applicable. Additionally, whether or not the vector field B exists depends on the vector field A and whether or not ∇⋅A=0.

- #1

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Assuming the system follows Maxwell's equations, what must both fields satisfy such that

##∇⋅(\frac{∂B}{∂t})=0## ?

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... and what do you get?

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that's what I'm wondering myselfSimon Bridge said:... and what do you get?

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If I don't see how you are attempting the problem I don't know how it is a problem for you so I don't know how to help you.

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Simon Bridge said:

If I don't see how you are attempting the problem I don't know how it is a problem for you so I don't know how to help you.

Oh I get it! Gauss' Law for Magnetic Flux! Right under my nose the whole time.

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Let's say we are given a vector field ##A##.

Vector field ##B## is defined as ##B = ∇×A##

Must ##∇⋅A=0## in order for ##B## to exist?

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https://en.wikipedia.org/wiki/Magnetic_potential#Maxwell.27s_equations_in_terms_of_vector_potential

The zero-divergence of rate of change of magnetic flux is a physical law that states that the net flow of magnetic field lines into any closed surface is zero. This means that the amount of magnetic flux entering a surface is equal to the amount of magnetic flux leaving the surface.

This law is important because it is a fundamental principle in electromagnetism and is essential for understanding and predicting the behavior of magnetic fields. It also has practical applications in various fields, such as in the design of electronic devices and magnetic sensors.

The zero-divergence of rate of change of magnetic flux is essentially the magnetic analogue of Gauss's law, which states that the net electric flux through a closed surface is equal to the enclosed electric charge. Both laws involve the concept of flux and show that the net flow of a certain quantity through a closed surface is zero.

No, zero-divergence of rate of change of magnetic flux is a fundamental law of electromagnetism and cannot be violated. In fact, it has been extensively tested and found to hold true in all observed cases.

This law can be expressed mathematically using the divergence theorem, which states that the flux of a vector field through a closed surface is equal to the volume integral of the field's divergence over the volume enclosed by the surface. In the case of magnetic flux, this integral will always equal zero, hence the law of zero-divergence.

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