1 Physics 2102 Gabriela González € B =µ0in € B (z) ≈µ02π µ z3µ=NiA An electrical current produces a magnetic field.2 dA 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 • 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”). Then a time varying magnetic FLUX creates an induced EMF, and thus an electrical current if the edge is a wire!: • 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!3 • A closed loop of wire encloses an area of 1 m2 in which in a uniform magnetic field exists at 300 to the PLANE of the loop. The magnetic field is DECREASING at a rate of 1T/s. The resistance of the wire is 10 Ω. • What is the induced current? 300 n Is it …clockwise or …counterclockwise? • 3 loops are shown. • B = 0 everywhere except in the circular region where B is uniform, pointing out of the page and is increasing at a steady rate. • Rank the 3 loops in order of increasing induced EMF. – (a) III, II, I – (b) III, (I & II are same) – (c) ALL SAME. I II III • Just look at the rate of change of ENCLOSED flux • III encloses no flux and it does not change. • I and II enclose same flux and it changes at same rate.4 • A square loop of wire of side L is rotated at a uniform frequency f in the presence of a uniform magnetic field B as shown. • Describe the EMF induced in the loop. B L θ B € = BL22πf( )sin(2πft)• An infinitely long wire carries a constant current i as shown • A square loop of side L is moving towards the wire with a constant velocity v. • What is the EMF induced in the loop when it is a distance R from the loop? L L v Choose a “strip” of width dx located as shown. Flux thru this “strip” R x5 L v R x What is the DIRECTION of the induced current? • Magnetic field due to wire points INTO page and gets stronger as you get closer to wire • So, flux into page is INCREASING • Hence, current induced must be counter clockwise to oppose this increase in flux. MagLev train relies on Faraday’s Law: currents induced in non-magnetic rail tracks repel the moving magnets creating the induction; result: levitation! Guitar pickups also use Faraday’s Law -- a vibrating string modulates the flux through a coil hence creating an electrical signal at the same frequency.6 • 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!) N S Pendulum had kinetic energy What happened to it? Isn’t energy conserved??7 • 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 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 • Breaking the circuit changes the current through “primary coil” • Result: LARGE change in flux thru secondary -- large induced
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