Physics 2102 Gabriela Gonz lez A magnetic field can create a en electrical current too If we define magnetic flux similar to definition of electric flux but for an open surface with an edge B n dA Then a time varying magnetic FLUX creates an induced EMF and thus an electrical current if the edge is a wire Take note of the MINUS sign The induced EMF acts in such a way that it OPPOSES the change in magnetic flux Lenz s Law When the N pole approaches the loop the flux into the loop downwards increases The loop can oppose this change if a current were to flow clockwise hence creating a magnetic flux upwards So the induced EMF is in a direction that makes a current flow clockwise If the N pole moves AWAY the flux downwards DECREASES so the loop has a counter clockwise current A non magnetic e g copper aluminum ring is placed near a solenoid What happens if There is a steady current in the solenoid The current in the solenoid is suddenly changed The ring has a cut in it The ring is extremely cold Drop a non magnetic pendulum copper or aluminum through an inhomogeneous magnetic field What do you observe Why Think about energy conservation Pendulum had kinetic energy What happened to it Isn t energy conserved N S The gap between the spark plug in a combustion engine needs an electric field of 107 V m in order to ignite the air fuel mixture For a typical spark plug gap one needs to generate a potential difference 104 V But the typical EMF of a car battery is 12 V So how does a spark plug work spark 12V Breaking the circuit changes the current through primary coil Result LARGE change in flux thru secondary large induced EMF The ignition coil is a double layer solenoid Primary small number of turns 12 V Secondary MANY turns spark plug http www familycar com Classroom ignition htm We saw that a time varying B n magnetic FLUX creates an induced EMF in a wire exhibited as a current Recall that a current flows in dA a conductor because of electric field Hence a time varying magnetic flux must induce an ELECTRIC FIELD Another of Maxwell s equations Closed electric field To decide SIGN of flux use right lines No potential hand rule curl fingers around loop flux thumb The figure shows two circular regions R1 R2 with radii r1 1m r2 2m In R1 the magnetic field B1 points out of the page In R2 the magnetic field B2 points into the page Both fields are uniform and are DECREASING at the SAME steady rate 1 T s Calculate the Faraday integral for the two paths shown Path II Path I R1 R2 I II A long solenoid has a circular cross section of radius R The current through the solenoid is increasing at a steady rate di dt Compute the variation of the electric field as a function of the distance r from the axis of the solenoid First let s look at r R R Next let s look at r R electric field lines magnetic field lines E r r r R Two versions of Faradays law A varying magnetic flux produces an EMF A varying magnetic flux produces an electric field
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