when a free rod of length L is made to traverse in xy with velocity v in a region containing uniform magnetic field in z direction, then according to the faraday's law emf = - B dA/dt

here neither the area of the rod if changing with respect to time, nor the magnetic field is changin w.r.t to time, then how come an emf is genereated ???

i know the other concept in which the magnetic field exerts a force F on the electroins due to which there is an eletric field, but please explain using the above !!

The electric fields and magnetic fields considered up to now have been produced by stationary charges and moving charges (currents), respectively. Imposing an electric field on a conductor gives rise to a current which in turn generates a magnetic field. One could then inquire whether or not an electric field could be produced by a magnetic field. In 1831, Michael Faraday discovered that, by varying magnetic field with time, an electric field could be generated. The phenomenon is known as electromagnetic induction. Figure 10.1.1 illustrates one of Faraday’s experiments. Figure 10.1.1 Electromagnetic induction Faraday showed that no current is registered in the galvanometer when bar magnet is stationary with respect to the loop. However, a current is induced in the loop when a relative motion exists between the bar magnet and the loop. In particular, the galvanometer deflects in one direction as the magnet approaches the loop, and the opposite direction as it moves away. Faraday’s experiment demonstrates that an electric current is induced in the loop by changing the magnetic field. The coil behaves as if it were connected to an emf source. Experimentally it is found that the induced emf depends on the rate of change of magnetic flux through the coil. 10-2 10.1.1 Magnetic Flux Consider a uniform magnetic field passing through a surface S, as shown in Figure 10.1.2 below: Figure 10.1.2 Magnetic flux through a surface Let the area vector be , where A is the area of the surface and its unit normal. The magnetic flux through the surface is given by A = A ˆ G n nˆ cos Φ = B B A⋅ = BA θ G G