# Faradays law and rate of change of flux

consider a table with the a uniform magnetic field of flux density B coming directly out of it, the field lines are perpendicular to the the surface of the table, pointing up and out. let a loop of wire enclosing area A lie on the surface of the table, then flux through the loop is AB. let me move the loop ALONG the table surface to another part of table in time T. since the field is uniform the flux through the loop here is also AB. By Faradays law the induced emf is rate of change of flux through loop which is (AB-AB)/T = 0. but how is this possible because the loop of wire which is the conductor clearly cuts the field lines as its moved along the surface of the table and hence there must be an induced emf right? what is going on?

For the line segment EF, this cuts the magnetic field and the emf induced along this segment is $$\epsilon = \frac{d B}{d t} = B l v,$$ where $l$ is the length of the line segment EF and you can use Fleming's right hand rule to determine the direction of the induced current which flows through the circuit.