electromagnetic induction

Electromagnetic Induction The phenomenon of production of induced emf (and hence induced current) due to a change of magnetic flux linked with a closed circuit is called electromagnetic induction.    The phenomenon in which electric current is generated by varying magnetic fields is appropriately called electromagnetic induction  

Magnetic Flux The magnetic flux through any surface placed in a magnetic field is the total number of magnetic lines of force crossing the surface normally.  It is a scalar quantity represented by fi ϕ or ϕB.  ϕ = B.A (dot product of B and A vectors) = B A cos theta Flux through whole area ϕ= ∫ over A:  B. dA  The SI unit of magnetic flux is weber (Wb) or tesla meter squared (T m2 ). And dimensions are [ML^2A^-1T^-2] 1 Wb = 10^8 maxwell If normal to the plane points in direction of field, flux is positive, if in the opposite, flux is negative.   

Laws of EMI Faraday's laws- give us the magnitude of induced emf Lenz law gives us the direction of induced emf.      Faraday's Laws First Law Whenever the magnetic flux linked with a closed circuit changes, an emf (and hence a current) is induced in it which lasts only so long as the change in flux is taking place. This phenomenon is called emi.  Second Law The magnitude of the induced emf is equal to the rate of change of magnetic flux linked with the closed surface.  |ε| = Δϕ/ Δt Taking Lenz law into account,  |ε| = - Δϕ/ Δt If the coil consists of N tightly wound turns, |ε| = - N Δϕ/ Δt If flux changes from ϕ1 to ϕ2 in time t seconds ε = - N ϕ2- ϕ1/ Δt   Volts   Induced Current Current produced in a conductor due to change in magnetic flux through the region is called induced current. If N is the number of turns and R is the resistance of a coil. The magnetic flux linked with its each turn changes by dФ in short time interval dt, then induced current flowing through the coil is I = |ε|/R = -1/R (N Δϕ/ Δt) Lenz's Law The direction of induced current is such that it opposes the cause which produces it i.e., it opposes the change in magnetic flux. The polarity of the induced emf is such that it tends to produce induced current in such a direction that it opposes the change in magnetic flux that produced it. a) When N pole of magnet is brought near the coil (right side) , IC flows away from it, i.e. in anticlockwise direction. The motion of the magnet increases the flux through the coil and the IC generates flux in opposite direction & hence opposes and reduces this flux. b) When N pole is brought away from the coil (right side), IC flows in the direction of it i.e. clockwise direction. The motion of the magnet decreases the flux throughout the coil. The IC generates flux in the same direction and hence increases the flux. Lenz’s law is a consequence of the law of conservation of energy.      

Motional EMF   The emf induced across ends of a conductor due to its motion in a magnetic field is called motional emf.    Suppose a conductor of length l and a length x of the closed loop (width) lies inside the magnetic field.  Then flux: phi= BA = Blx Acc. to Faraday. ε = -d phi/dt = -d/dt (Blx) = -Bl dx/dt = Blv Where dx/dt= -v since the velocity is in decreasing direction of x Induced emf is called motional because it is induced due to the motion of the conductor in a mag. field.            

Eddy Currents Discovered by Foucault, aka Foucault's Currents. Eddy cause they look like eddies or whirl-pools in water Eddy currents are the currents induced in solid metallic masses when the metallic flux threading through them changes.  it is found that the motion of a copper plate pendulum is damped and in a little while the plate comes to a halt in the magnetic field. Magnetic flux associated with the plate keeps on changing as the plate moves in and out of the region between magnetic poles. The flux change induces eddy currents in the plate. Directions of eddy currents are opposite when the plate swings into the region between the poles and when it swings out of the region area available to the flow of eddy currents is less in the pendulum plate with holes or slots and thus reduces electromagnetic damping and the plate swings more freely Eddy currents are undesirable since they heat up the core and dissipate electrical energy in the form of heat. They are produced inside the iron cores of rotating armatures and dynamos and cores of transformers. They might even damage the insulation of coils.    Eddy currents are minimised by using laminated cores which consist of thin sheets of metal insulated from each other by a thin layer of varnish like lacquer. The planes of these sheets are placed perpendicular to the direction of currents. This arrangement reduces the strength of the eddy currents.   Applications :  Magnetic brakes in trains : Strong electromagnets are situated above the rails in some electrically powered trains. When the electromagnets are activated, the eddy currents induced in the rails oppose the motion of the train. As there are no mechanical linkages, the braking effect is smooth. Electromagnetic Damping: Certain galvanometers have a fixed core made of nonmagnetic metallic material. When the coil oscillates, the eddy currents generated in the core oppose the motion and bring the coil to rest quickly. Induction furnace : Induction furnace can be used to produce high temperatures and can be utilised to prepare alloys, by melting the constituent metals. A high frequency alternating current is passed through a coil which surrounds the metals to be melted. The eddy currents generated in the metals produce high temperatures sufficient to melt it. Electric power meters: The shiny metal disc in the electric power meter (analogue type) rotates due to the eddy currents. Electric currents are induced in the disc by magnetic fields produced by simultaneously varying currents in a coil.          

Inductance flux linkage- NΦB for a closely wound coil of N turns.\ flux ΦB α I  and phi B/ dt is directly proportional to dI/dt NΦB ∝ I where N turns ......................................... eq. Inductance is a scalar quantity. It has the dimensions of [M L 2 T –2 A –2] SI unit is henry denoted by H It is the constant of proportionality in the above eq.       

Mutual Inductance In mutual inductance there are 2 coils, current is passed in one coil, as current increases there is change in the flux, and as a result current is induced in the second coil. Consider coil 1 connected to battery and coil 2 is connected to the galvanometer. When the key is pressed attached to the coil 1 the current starts flowing, when the current starts increasing flux linked also starts increasing. Because of the increase in the flux linked with the coil1, the flux of coil 2 also increases. There is change in the flux of the coil 2 as a result emf is induced in the coil 2. Because of the induced emf induced current will be there in coil2. This induced current opposes the increase of the current in coil 1. M12 is called the mutual inductance of solenoid S1 with respect to solenoid S2 . It is also referred to as the coefficient of mutual induction.   Φ(2)∝ I(1) =>Φ(2) = MI(1)where M = constant of proportionality known as Mutual Inductance. Induced emf in coil 2 e=-(dΦ(2)/dt) =>e =-d/dt(MI (1)) where I current flowing in coil (1). Therefore e =-d/dt (M I (1)) M21 = µ0 n1 n2 πr 2 1 l M12 = M21= M  Instead, if a medium of relative permeability µr had been present, the mutual inductance would be M =µr µ0 n1 n2 π r 2 1 l  

Self- Inductance   N phi B = LI where L is self inductance It is also called the coefficient of self-induction of the coil the self-induced emf always opposes any change (increase or decrease) of current in the coil. emf = - L dI/dt total mag. fiel B = µ0 n I (neglecting edge effects, as before). The total flux linked with the solenoid is N phi B= (nl) (u0 n i) (A) = u0 n^2 l i A nl is the total no. of turns thus, L = N phi B/ current I = u0 n^2 lA for some other material with permeability ur, L = u0 ur n^2 lA self-inductance of the coil depends on its geometry and on the permeability of the medium. The self-induced emf is also called the back emf as it opposes any change in the current in a circuit. Physically, the self-inductance plays the role of inertia the energy required to build up the current I is, W= 1/2 L I^2 (I= current)