(i) Motion of conduction wire in a magnetic field. Imagine a small piece of metal wire being dragged across in between the pole pieces of a magnet as shown in Fig. A conductor consists of large no. of free electrons. These electrons can move freely inside the metal under the slightest force. The electrons in the metal wire will move along the wire, and direction of force acting on electron is given by equation
Net positive and negative charges will accumulate at the ends of the wire creating an electric field that will cause a force on the electrons in a direction that is opposite to the direction of the Lorentz force. Clearly, when a certain amount of accumulation of charges has taken place such that the electric force and the magnetic Lorentz force cancel, there will be no further movement of the ‘free’ electrons. The two ends of the wire thus become like the two terminals of a battery without any external connection.
Let V = P.D or induced e.m.f. developed across the ends of the conductor
∴ Electric field,
E = \(\frac{V}{I}\)
Force on electron due to electric field
F' = eE = \(\frac{eV}{l}\)
But F' = F
\(\frac{eV}{l}\) = Bev
∴ V = B l v
This is the e.m.f. induced across the two ends of the conductor.
(ii) A closed loop moving completely in magnetic field. Fig. shows a closed rectangular loop PQRS of metallic wire held horizontally in a uniform magnetic field \(\vec B\) acting ⊥ to the plane of the loop.
When the loop is dragged horizontally to the left with a velocity v, Lorentz force acts on the electrons in arms PQ and RS. Therefore, negative charges accumulate on QR and positive charges accumulate on PS, assuming that the loop is completely within the magnetic field. Though QR and PS are connected by conducting wires PQ and RS yet no flow is possible because a continuous path for the flow of electrons is not available, Fig.
(iii) A closed loop moving partially in a magnetic field. Suppose a part PQR'S' is inside the magnetic field and portion R'S'SR is just outside the field. R'S' is another wire connecting QR and PS, Fig. The negative charges accumulated on R' and positive charges accumulated on PS find a conducting path S'SRR’S’ for their continuous flow. Therefore, current begins to flow in this loop as is indicated by galvanometer G. This is the induced current.
