Electromagnetic Induction 1 Induced emf and Magnetic Flux We have seen that electric currents produce magnetic fields Can magnetic fields produce electric currents Faraday s experiment see micro magnet fsu edu electromag java faraday When the switch is closed or opened the compass in the second coil shows a brief deflection and then returns to zero When the switch is opened the compass deflects in the opposite direction and returns then to zero If there is a constant current in the primary coil no signal is detected Conclusion A changing magnetic field produces an electric current in the second coil The magnetic field created by the electric current is detected by the compass Dr D Wackeroth Spring 2005 PHY102A Electromagnetic Induction In order to understand this phenomenon we need the concept of magnetic flux Consider a loop of wire in the presence of a uniform magnetic field B The loop has an area A The magnetic flux is defined as BA cos 1 and the normal perpendicular to the loop where is the angle between B The SI unit of the magnetic flux is the weber Wb 1 W b 1 T m2 Dr D Wackeroth Spring 2005 PHY102A Electromagnetic Induction Remarks The value of the magnetic flux is proportional to the number of field lines passing through the loop If the field lines are parallel to the loop 90 cos 0 and 0 The flux is maximal when the lines are perpendicular to the loop 0 i e cos 1 and BA Dr D Wackeroth Spring 2005 PHY102A Electromagnetic Induction 2 Faraday s Law of Induction Experiment Consider a wire loop connected to a galvanometer If a magnet is moved toward the loop the galvanometer needle deflects Result A current is set up in the circuit as long as there is relative motion between magnet and loop Such a current is called an induced current The average emf induced in a circuit equals the rate of change of magnetic flux through the circuit Remark There is no battery here Dr D Wackeroth Spring 2005 PHY102A Electromagnetic Induction If a circuit contains N tightly wound loops and the flux through each loop changes by an amount during the time interval t the average induced emf in the circuit is given by Faraday s law of magnetic induction N t 2 Note the minus sign The polarity of the induced emf is such that it produces a current whose magnetic field opposes the change in magnetic flux through the loop Lenz s law In other words The induced current tends to maintain the original flux through the circuit Dr D Wackeroth Spring 2005 PHY102A Electromagnetic Induction 3 Motional emf Consider a straight conductor of length L moving with constant velocity through a uniform magnetic field The electrons experience a force of magnitude F qvB Because of the magnetic force electrons accumulate at the lower end a corresponding positive charge is created at the upper end Dr D Wackeroth Spring 2005 PHY102A Electromagnetic Induction Because of the charge an electric field is created F qE qvB or E vB is constant The potential difference across the ends is E V EL BLv 3 A potential difference is maintained across the conductor as along as there is motion through the magnetic field If the motion is reversed the polarity of the potential difference is also reversed If the moving conductor is part of a closed conducting path a motional emf is created and a current is flowing Assume that the conductor is moving a distance x in a time interval t The change of flux is then BA BL x Dr D Wackeroth Spring 2005 PHY102A Electromagnetic Induction From Faraday s law one then finds for the motional emf x B BLv t t 4 Direction of the current Lenz s law implies that the induced current must be in a direction such that the flux it creates opposes the change in the external flux If the field is directed into the paper the current produces a flux out of the paper Or the force on the current in the external magnetic field has to oppose the direction of motion conservation of energy From right hand rule current counter clockwise clockwise if the conductor moves to the right left Dr D Wackeroth Spring 2005 PHY102A Electromagnetic Induction Dr D Wackeroth Spring 2005 PHY102A Electromagnetic Induction 4 The Electric Generator Generators and electric motors operate on the principle of electromagnetic induction Alternating Current AC Generator The AC generator is a device which converts mechanical energy into electrical energy In its simplest form it consists of a coil of wire rotated in a uniform magnetic field by some external mechanical means emf generated by the loop BLv where v is the component of field v v sin Here the velocity vector perpendicular to the B is the angle of the velocity vector v and the magnetic field vector B Dr D Wackeroth Spring 2005 PHY102A Electromagnetic Induction emf induced in the rotating coil 2BLv 2BLv sin factor 2 there are two sides of the loop which contribute Dr D Wackeroth Spring 2005 PHY102A Electromagnetic Induction If the loop rotates with constant angular velocity v r t and the area of the loop is A L2r 2BLr sin t BA sin t If the loop has N turns N BA sin t 5 The emf varies sinusoidally with time the emf changes polarity as the coil rotates in a closed circuit an alternate current results Dr D Wackeroth Spring 2005 PHY102A