EEE107 Electromagnetic Induction

Electromagnetic induction through flux cutting S bar magnet coil Galvanometer

Requirements for Induced EMF For an emf to be induced in a conductor there must be a changing magnetic field; that is, relative motion between the conductor and the magnetic flux. In other words, the conductor must cut the magnetic flux or the magnetic flux must cut the conductor. In addition, it can be demonstrated that a larger emf is produced if: the magnet or coil is moved faster the number of windings of the coil is increased a stronger magnet is used In other words, the induced emf depends on the strength of the magnetic field, the rate at which the flux cuts (or is cut by) the conductor and the number of turns in the coil. The direction of the induced emf (direction of current flow) depends on the polarity of the magnet and its direction of movement relative to the coil.

Electromagnetic induction through flux linkage Coil 1 Coil 2 ferromagnetic material It may be observed that a momentary deflection of the galvanometer occurs when the current in coil 1 is switched on. A momentary deflection in the opposite direction is observed when the current is switched off. No deflection is observed when the current in coil 1 is steady. From these observations, we may conclude that an emf is induced in coil 2 due to a changing current in coil 1.

Faraday’s Law of Electromagnetic Induction Faraday’s law states that the emf, e, induced in a circuit is proportional to the rate of change of flux linkage, where flux linkage is the product of the magnetic flux through the circuit and the number of turns N affected by the flux. Mathematically, we may say that: e  d/dt(N) or e  N.d/dt, since N is normally constant. If the flux, , is measured in webers and t is measured in seconds, then Faraday’s law may be summarised as:

Lenz’s Law of Electromagnetic Induction Faraday’s law gives the magnitude of the induced emf only. Its direction is given by Lenz’s law, which states that the direction of the induced emf is such that it opposes the cause which produces it. For example, an increasing flux through a closed circuit will induce an emf (and hence a current in the circuit) that generates a magnetic field which tries to stop the increase in flux; that is, it opposes the applied field (cause) that produces the emf. Conversely, a decreasing flux will induce an emf and hence a current that tries to increase the applied field, and stop it decreasing. Lenz’s law can be combined with Faraday’s law into a single equation that gives both the magnitude and direction of induced emf:

Example Calculate the average emf induced in a coil of 500 turns when the flux linking it changes from 0.5mWb to 1mWb in 1 millisecond. Solution If the flux change is non-uniform and changes from an initial valuei to a final value (f in a time of t, to average rate of change of flux is (f - i )/t Thus the average induced emf is given by the expression: e = -N(f - i)/t e = -N(f - i)/t volts where: N = 500 turns f = 10-3 Wb i = 0.5 × 10-3 Wb t = 0.001 s e = -500(1 × 10-3 - 0.5 × 10-3)/10-3 = -250V

Simple Transformer Primary windings (Np turns) ~ Primary windings (Np turns) Secondary windings (Ns turns) Transformer core Coil 1 Coil 2 ac voltage source

Ideal Transformer primary input power = secondary output power If we assume that the transformer is 100% efficient, i.e. there is no power loss, then the input (primary) electrical power must equal the output (secondary) power. A transformer will never be 100% efficient as there will be power loss due to, e.g. heat generation due to the resistance of the windings and hysteresis effects. For an ideal transformer we can say that power in primary = power in secondary or Ep  Ip = Es × Is where Ip and Is are the primary and secondary currents respectively. Therefore

Let Ep = peak value of voltage applied to primary An alternating source of emf with peak value 200V is applied to the primary winding of a transformer. If the number of turns in the primary and secondary windings are 500 and 25 respectively, calculate the peak value of the voltage induced in the secondary winding. What is the value of the secondary current if the primary current is 5mA? Let Ep = peak value of voltage applied to primary Es = peak value of voltage applied to secondary Np = number of turns on primary Ns = number of turns on secondary Es/Ep = Ns/Np Es = Ns/Np × Ep Therefore: Es = (25/500) × 200 = 10V Is = Np/Ns × Ip = (500/25) × 5mA = 0.1A.