QUESTION 3 is .... Considering the right side of show that The next of Maxwell\'

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QUESTION 3 is

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Considering the right side of show that The next of Maxwell's Laws is due to the English physicist Michael Faraday (1791-1867), who discovered that if a loop of conducting wire is placed in a changing magnetic field, then an electric current is generated in the wire (this law is the basis for electrical generators). In integral form Faraday's Law states that where C is the closed curve corresponding to the wire loop and 5 is a surface with C as its boundary Assume that in general the magnetic field B depends on x, y, z, and t (time). Use Stokes' Theorem to show that the differential form of this law is (Assume that the order of integration and differentiation may be switched.) Explain why if the magnetic field does not vary in time, no current is generated.

Explanation / Answer

Using the Leibnitz rule for derivatives of integrals, you can take that derivative inside the integral sign, as the variable w.r.t. which it is derivated is different from the one which is under integral. So, dB/dt is a constant, so the integral is just for dS, which is definitely a*deltaZ (the area of the loop C).

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