![]() dB/dt (through a fixed area) -around loopEdr(at a fixed time) The minus sign in this equation tells us about the direction of (See below.) When the magnetic flux through the area enclosed by the loop changes, around loopEdris not zero, the electric field Ecirculates. In this case, the magnetic behavior of the material is said to be nonlinear. The negative sign indicates that the induced emf always opposes the time-varying magnetic flux. The equation below expresses Faraday's law in mathematical form. 12.17 This equation becomes B 0 n I / ( 2 R) for a flat coil of n loops per length. 12.16 By setting y 0 in Equation 12.16, we obtain the magnetic field at the center of the loop: B 0 I 2 R j. The concept of magnetic field intensity also turns out to be useful in a certain problems in which \(\mu\) is not a constant, but rather is a function of magnetic field strength. For this example, A R 2 and n j, so the magnetic field at P can also be written as B 0 I j 2 ( y 2 R 2) 3 / 2. ![]() Where B is the magnetic flux density, () is the magnetic flux and. \), then only the perpendicular component of the magnetic field is constrained. The magnetic field can be pulled out of the integration, leaving the flux as the product of the magnetic field times area. Magnetic flux per unit area is called magnetic flux density.
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