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What are the Simplifying Assumptions for Calculating Eddy Current Forces?
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[QUOTE="LeafNinja, post: 6516836, member: 644741"] Faraday's law is represented in derivative form as $$\nabla \times \vec{E} = -\frac{d\vec{B}}{dt}$$ In integral form, this is $$\int_{closedloop} \vec{E} \bullet dl = -\frac{d\Phi_{B}}{dt}$$ Where ##\Phi_{B}## is the magnetic flux or integral of the magnetic flux density over the cross section and ##\int_{closedloop} \vec{E} \bullet dl## is the integral of the electric field around a closed loop. The - sign indicates that if your are facing the coil and the magnetic field lines are going through the coil pointing towards you, the E-field lines will travel clockwise. The equations 1. and 2. that you presented use E for the emf which is generally equal to the voltage such as in a battery. Another way to think of it is ##V = \int_{coilpath} \vec{E} \bullet dl ## where ##V## is the voltage. The N simply indicates that there are N turns of the coil. This is approximated by using Faraday's law on N closed loops. So ##N\int_{closed loop} \vec{E} \bullet dl = E = V = -N\frac{d\Phi_{B}}{dt}## becomes larger (There are N loops or turns, so given a uniform magnetic field, the electromotive force becomes N times as large as it would have been had there only been 1 turn). So the second equation is more correct. Regarding your question about derivatives, ##\frac{\Delta y}{\Delta t}## indicates finite differences (eg. how far did a frog move in one second). ##\frac{dy}{dt}## indicates derivatives (how far the frog is moving per second at this instant in time) ##\frac{\partial y}{\partial t}## indicates the change in the dependent variable given that only 1 indpendent variable is changing. Eg. If the frog's position depends on both the snake position x and the time t, $$\frac{dy}{dt} = \frac{\partial y}{\partial x}\frac{\partial x}{\partial t} + \frac{\partial y}{\partial t}$$ So ##\frac{\partial y}{\partial t}## is the rate at which the frog's position would change if the snake was not moving. In this case either the derivative or partial derivative would work because there is only 1 independent variable: time. [/QUOTE]
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What are the Simplifying Assumptions for Calculating Eddy Current Forces?
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