A loop is made from a conductive wire. The wire moves, so the area inside the loop is time dependent: S=S(t) There is a constant homogeneus magnetic field B directed perpendicular to the wire and we are supposed to calculate induced voltage. In my opinion there is no electric field and no voltage, since there field B is constant. However there is a magnetic force experienced by charges moving in magnetic field: Method 1: F=e*B*v If this force is integrated over the loop to gain work on a charge e after 1 circle, we get: A=-e*B*dS/dt The proposed solution used Faraday's law of induction: Method 2: U=-dfi/dt=-d(B*S)/dt=-B*dS/dt I think that this is a misuse of the law, since corresponding Maxwell's equation can be used only for fixed loop, but changing magnetic field. However the work gained by a charge completing one circle is exactly the same as with previous method: A=e*U=-e*B*dS/dt My question is: Is the method 2 realy incorrect? If yes, why is the work the same? If no, how do we prove that Faraday's law can be used in case of constant B and changing loop area?