Yes, it is ##\phi =\iint_{S}B\cdot dS##TSny said:Can you give us the explicit expression for the integral form? Does the integrand have a dot product of vectors?
So you are saying that it is implied due to the dot product, but just not shown in the equation. I am not sure I fully understand what is going on, but I get what you are saying.Delta2 said:Yes, @TSny implies that the ##\cos\theta## term is hidden inside the dot product of the vectors. But is not a constant term like it is in the case of a uniform magnetic field and a plane surface, it varies as we move from point to point on the surface, which is what makes the integration difficult.
Yes well you wrote correctly the formula at post #4, but the whole point there is that ##B\cdot dS## is a very cute and compact formalism that hides a mini can of worms underneath: If you want to exactly write its equal expression using cosine of angle its a kind of trouble.Einstein44 said:So you are saying that it is implied due to the dot product, but just not shown in the equation. I am not sure I fully understand what is going on, but I get what you are saying.
Yes. Note that for a uniform B field, you can write the flux in terms of a dot product as ##\Phi = B S \cos \theta = \vec B \cdot \vec S## where in the last expression the ##\cos \theta## is "hidden" in the dot product. You just want to make sure that you understand the meaning of an area vector.Einstein44 said:So you are saying that it is implied due to the dot product, but just not shown in the equation.
Got it, thanks!TSny said:Yes. Note that for a uniform B field, you can write the flux in terms of a dot product as ##\Phi = B S \cos \theta = \vec B \cdot \vec S## where in the last expression the ##\cos \theta## is "hidden" in the dot product. You just want to make sure that you understand the meaning of an area vector.
The magnetic flux equation in integral form is given by: Φ = ∫S B ⋅ dA, where Φ is the magnetic flux, B is the magnetic field, and dA is the differential area vector.
The magnetic flux equation is derived from Faraday's law of induction, which states that the induced electromotive force (EMF) in a closed loop is equal to the negative rate of change of magnetic flux through the loop. By integrating this equation over a surface, we get the magnetic flux equation in integral form.
The magnetic flux equation is important in understanding the relationship between magnetic fields and induced EMF. It is also used in calculations for magnetic circuits and in the study of electromagnetic waves.
The magnetic flux equation is analogous to Gauss's law in electrostatics, where the electric flux is given by ΦE = ∫S E ⋅ dA. Both equations represent the total amount of the respective field passing through a surface.
Yes, the magnetic flux equation can be rearranged to solve for the magnetic field B. However, it is not always the most efficient method for calculating the magnetic field and other equations, such as Ampere's law, may be more appropriate in certain situations.