Question

Calculate induced EMF in a moving conductor in a uniform magnetic field

Answer 1

Electromagnetic induction. Emf induced in a moving conductor.Faraday’s law. Lenz’s law. Self-induction. Self-induced emf. Self-inductance of a coil of n turns.Energy stored in an inductor. Electrical oscillations. Electric generator, motor.







Electromagnetic induction. A great milestone occurred when Hans Christian Oersted discovered in 1819 a connection between electricity and magnetism in the form of a magnetic field near a current-carrying wire. Another great milestone occurred 12 years later in 1831 when Michael Faraday discovered another phenomenon relating electricity and magnetism: He discovered a phenomenon called electromagnetic induction. This discovery made possible a method for the generation of large amounts of electricity by mechanical means in the form of the electric generator --- which then ushered in a great revolution in our way of living in the form of our age of electricity. Let us learn more about this phenomenon that he discovered. Let us connect a conducting rod C to a sensitive galvanometer, as shown in Fig. 1, and pass the rod down between the poles of a horseshoe magnet. When we do this, a deflection of the galvanometer needle occurs, indicating a current. What a remarkable phenomenon! Who would expect such a thing?! When the rod is held stationary in the field, no current flows. Current only flows when the rod is moving within the magnetic field. When the rod is moved upward within the field, current flows in the opposite direction from which it flows when the rod is moved down. In addition, we discover that the faster the rod is passed through the field, the greater is the deflection of the needle. Thus moving the rod quickly through the field gives a greater current. Let us move the rod laterally between the poles, parallel to the flux lines. No current flows when we do this. Current only flows when we cut across flux lines. Let us consider another experiment. Let us connect a galvanometer to a spool of insulated wire as shown in Fig. 2 and plunge a bar magnet down inside the hole in the spool. Again, the galvanometer needle deflects, indicating a current. When the magnet is withdrawn, the galvanometer indicates a current in the opposite direction. The faster it is plunged down, the stronger is the current produced. When the flux lines of the magnet cross the wire in the coils, current is produced.

 

When a conductor cuts through lines of magnetic flux or when the magnetic flux field changes in strength around a conductor, an emf is generated (induced) in the conductor. This emf is called aninduced emf. If the conductor forms part of a circuit, as in the above cases where it is connected to a galvanometer, that emf produces a current. The current is called aninduced current. The phenomenon we are talking about is called electromagnetic induction.