![]() There is current and thus we must still be having a change in flux in the negative direction. Yet, from experiment we know this is not true. If you claim the flux increases (positively) after the point where it is zero, then what you are saying is that the change in magnetic flux is zero at that point and hence the induced current is zero. It says that the loop in your diagram will induce an electric current in the direction that opposes the change in magnetic flux. However, in order for our mathematical formulation of magnetism to be consistent it is important. You might think this is an unnecessary distinction. Your confusion comes from not taking into account that the area we choose must be directed in some way. Lastly, we include the number of turns in the coil to. The only quantity varying in time is the current, the rest can be pulled out of the time derivative. Faraday’s law involves a time derivative of the magnetic flux. The coil is then rotated through an angle of 30° about axis PQ. Therefore, the magnetic flux through the coil is the product of the solenoid’s magnetic field times the area of the coil. The coil is in a uniform magnetic field of flux density B with its plane parallel to the field lines. ![]() ![]() It is clear mathematically from the dot product that $\Phi$ can be positive (when area and flux are in same relative direction) or negative( when they are in opposite directions). A rectangular coil of area A has N turns of wire. The equation for magnetic flux is $$ \Phi = \vec B \cdot d\vec A = BAcos\theta$$, where both the magnetic flux density and the area are vectors. The magnetic flux is the amount of field lines (the magnetic flux density) going through a given area. ![]()
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