Chapter 29 – Electromagnetic Induction- Induction Experiments - Faraday’s Law- Lenz’s Law- Motional Electromotive Force- Induced Electric Fields- Eddy Currents- Displacement Current and Maxwell’s Equations- Superconductivity1. Induction Experiments (Faraday / Henry)- If the magnetic flux through a circuit changes, an emf and a current are induced.- A time-varying magnetic field can act as source of electric field.- A time-varying electric field can act as source of magnetic field.Maxwell- An induced current (and emf) is generated when: (a) we move a magnet around a coil, (b) move a second coil toward/away another coil, (c) change the current in the second coil by opening/closing a switch.2. Faraday’s Law- Magnetically induced emfs are always the result of the action of non-electrostatic forces. The electric fields caused by those forces are En(non-Coulomb, non conservative).∫∫⋅=⋅=Φ dABAdBBϕcosMagnetic flux: ϕcos⋅⋅=⋅=Φ ABABBIf B is uniform over a flat area A:Faraday’s Law of Induction: - The induced emf in a closed loop equals the negative of the time rate of change of the magnetic flux through the loop.dtdBΦ−=ε- Increasing flux  ε < 0 ; Decreasing flux  ε > 0- Direction: curl fingers of right hand around A, if ε > 0 is in same direction of fingers (counter-clockwise), if ε < 0 contrary direction (clockwise).- Only a change in the fluxthrough a circuit (not flux itself) can induce emf. If flux is constant  no induced emf.- If the loop is a conductor, an induced current results from emf. This current produces an additional magnetic field through loop. From right hand rule, that field is opposite in direction to the increasing field produced by electromagnet. dtdNBΦ−=εCoil:N = number of turnsEx: 29.4 - Generator I: a simple alternatorExs: 29.6, 29.7 - Generator III: the slide wire generator3. Lenz’s LawThe direction of any magnetic induction effect is such as to oppose the cause of the effect.- Alternative method for determining the direction of induced current or emf. -The “cause” can be changing the flux through a stationary circuit due to varying B, changing flux due to motion of conductors, or both.- If the flux in an stationary circuit changes, the induced current sets up a magnetic field opposite to the original field if original B increases, but in the same direction as original B if B decreases. - The induced current opposes the change in the flux through a circuit (not the flux itself).- If the change in flux is due to the motion of a conductor, the direction of the induced current in the moving conductor is such that the direction of themagnetic force on the conductor is opposite in direction to its motion (e.g. slide-wire generator). The induced current tries to preserve the “status quo”by opposing motion or a change of flux.B induced downward opposing the changein flux (dΦ/dt). This leads to induced current clockwise.Lenz’s Law and the Response to Flux Changes- Lenz’s Law gives only the direction of an induced current. The magnitude depends on the circuit’s resistance. Large R  small induced I  easier tochange flux through circuit. - If loop is a good conductor  I induced present as long as magnet moves with respect to loop. When relative motion stops  I = 0 quickly (due to circuit’s resistance).- If R = 0 (superconductor)  I induced (persistent current) flows even after induced emf has disappeared (after magnet stopped moving relative to loop).The flux through loop is the same as before the magnet started to move flux through loop of R =0 does not change.Magnetic levitation:-The principle of levitation is Lenz' rule. 1) The magnetic field created by the induced current in a metallic sample due to time-fluctuation of the external magnetic field of the coil wants to avoid its cause (i.e., the coil's fluctuating magnetic field). 2) Thus, the induced magnetic field in the sample and the external fluctuatingmagnetic field of the coil repel each other.3) The induced magnetic field (and the sample) move away from its cause, i.e. away from the coil's magnetic field. Then, for a conical coil (smaller radius at the bottom than at the top) the metallic sample will move upward due to this levitation force, until the force of gravity balances the force of levitation. (The levitation force is larger at the bottom of the conical coil than at the top of the coil).Induced Current / Eddy current levitation: - The rail and the train exert magnetic fieldsand the train is levitated by repulsive forcesbetween these magnetic fields. - B in the train is created by electromagnetsor permanent magnets, while the repulsiveforce in the track is created by a induced magnetic field in conductors within the tracks. - Problems: (1) at slow speeds the current induced in the coils of the track’s conductors and resultant magnetic flux is not large enough to support the weight of the train. Due to this, the train needs wheels (or any landing gear) to support itself until it reaches a speed that can sustain levitation. (2) this repulsive system creates a field in the track (in front and behind the lift magnets) which act against the magnets and creates a “drag force”. This is normally only a problem at low speed.4. Motional Electromotive ForceBvqF×=- A charged particle in rod experiences a magnetic force that causes free charges in rod to move, creating excess charges at opposite ends. - The excess charges generate an electric field (from a to b) and electric force (F = q E) opposite to magnetic force. - Charge continues accumulating until FEcompensates FBand charges are in equilibrium  q E = q v B- If rod slides along stationary U-shaped conductor  no FB acts on charges in U-shaped conductor, but excess charge at ends of straight rod redistributes along U-conductor, creating an electric field.LBvLEVab⋅⋅=⋅=RvBLRI ==ε∫⋅×= ldBv)(εldBvd⋅×= )(ε-The electric field in stationary U-shaped conductor creates a current moving rod became a source of emf (motional electromotive force). Withinstraight rod charges move from lower to higher potential, and in the rest ofcircuit from higher to lower potential.Induced current:vBL=εLength of rod and velocity perpendicular to B.- The emf associated with the moving rod is equivalent to that of a battery with positive terminal at a and negative at b. Motional emf: general form (alternative expression of