Electromagnetic Inductionpreviously:now:a definition: magnetic fluxexample: magnetic fluxFaraday’s law:changing the magnetic fluxexampleFaraday’s law for multiple loopslon-capafirst magnitude, now the direction…Lenz’s LawLenz’s law IIleft-hand rulesBe carefuldemo magnet through cooled pipequestionlon-capaEddy current+demoapplications of eddy currentsA moving barlon-capaDoing workgenerating current.Time varying voltagequestionSelf inductanceSelf inductance IIinduction of a solenoidexampleAn RL circuitRL Circuit IIquestionexamplelon-capaElectromagnetic InductionPHY232Remco [email protected] W109 – cyclotron buildinghttp://www.nscl.msu.edu/~zegers/phy232.htmlPHY232 - Remco Zegers Electromagnetic Inductions 2previously:¾ electric currents generate magnetic field. If a current is flowing through a wire, one can determine the direction of the field with the (second) right-hand rule:¾ and the field strength with the equation: B=μ0I/(2πR)¾ For a solenoid or a loop (which is a solenoid with one turn): B=μ0IN/(2R) (at the center of the loop)If the solenoid is long: B=μ0In (at the center of the solenoid)PHY232 - Remco Zegers Electromagnetic Inductions 3now:¾ The reverse is true also: a magnetic field can generate an electrical current¾ This effect is called induction: In the presence of a changing magnetic field, and electromotive force (voltage) is produced.demo: coil and galvanometerApparently, by movingthe magnet closer to the loop, a current is produced. If the magnet is held stationary,there is no current.PHY232 - Remco Zegers Electromagnetic Inductions 4a definition: magnetic flux¾ A magnetic field with strength B passes through a loop with area A¾ The angle between the B-field lines and the normal to the loop is θ¾ Then the magnetic flux ΦBis defined as:Units: Tm2or Weber (W)lon-capa uses WbPHY232 - Remco Zegers Electromagnetic Inductions 5example: magnetic flux¾ A rectangular-shaped loop is put perpendicular to a magnetic field with a strength of 1.2 T. The sides of the loop are 2 cm and 3 cm respectively. What is the magnetic flux?¾ B=1.2 T, A=0.02x0.03=6x10-4m2, θ=0.¾ ΦB=1.2 x 6x10-4 x 1 = 7.2x10-4Tm¾ Is it possible to put this loop such that the magnetic flux becomes 0?¾ a) yes¾ b) noPHY232 - Remco Zegers Electromagnetic Inductions 6Faraday’s law:¾ By changing the magnetic flux ΔΦBin a time-period Δt a potential difference V (electromagnetic force ε) is producedWarning: the minus sign is never used in calculations. It isan indicator for Lenz’s law which we will see in a bit.PHY232 - Remco Zegers Electromagnetic Inductions 7changing the magnetic flux¾ changing the magnetic flux can be done in 3 ways:¾ change the magnetic field¾ change the area¾ changing the anglePHY232 - Remco Zegers Electromagnetic Inductions 8examplex x x xx x x xx x x x¾ a rectangular loop (A=1m2) is moved into a B-field (B=1 T) perpendicular to the loop, in a time period of 1 s. How large is the induced voltage?• While in the field (not moving) the area is reduced to 0.25m2 in 2 s. What is the induced voltage? •This new coil in the same field is rotated by 45oin 2 s. What is the induced voltage?PHY232 - Remco Zegers Electromagnetic Inductions 9Faraday’s law for multiple loops¾ If, instead of a single loop, there are multiple loops (N), the the induced voltage is multiplied by that number:N Sresistor Rdemo: loops.If an induced voltage is put overa resistor with value R or theloops have a resistance, a currentI=V/R will flowPHY232 - Remco Zegers Electromagnetic Inductions 10lon-capa¾ You should now try problems 2,3,4 & 7 from lon-capa set 6.PHY232 - Remco Zegers Electromagnetic Inductions 11first magnitude, now the direction…¾ So far we haven’t worried about the direction of the current (or rather, which are the high and low voltage sides) going through a loop when the flux changes…N Sresistor Rdirection of I?PHY232 - Remco Zegers Electromagnetic Inductions 12Lenz’s Law¾ The direction of the voltage is always to oppose the change in magnetic fluxwhen a magnet approaches theloop, with north pointing towardsthe loop, a current is induced. As a results a B-field is made by theloop (Bcenter=μ0I/(2R)), so that the fieldopposes the incoming field madeby the magnet.Use right-hand rule: to make a field that is pointing up, the current must go counter clockwiseThe loop is trying to push the magnet awaydemo: magic loopsPHY232 - Remco Zegers Electromagnetic Inductions 13Lenz’s law II¾ In the reverse situation where the magnet is pulled away from the loop, the coil will make a B-field that attracts the magnet (clockwise). It opposes the removal of the B-field. magnet approaching thecoilmagnet moving away from the coil BmagnetBinduced BmagnetBinducedvvPHY232 - Remco Zegers Electromagnetic Inductions 14left-hand rules¾ There are several variations of left hand-rules available to apply Lenz’s law on different systems. If you know them, feel free to use it. However, they can be confusing and I will refrain from applying them.PHY232 - Remco Zegers Electromagnetic Inductions 15Be careful¾ The induced magnetic field is not always pointing opposite to the field produced by the external magnet.x x x xx x x xx x x xIf the loop is stationary in a field, whose strength is reducing, it wants to counteract that reduction by producing a field pointinginto the page as well: current clockwisePHY232 - Remco Zegers Electromagnetic Inductions 16demo magnet through cooled pipe¾ when the magnet passes through the tube, a current is induced such that the B-field produced by the current loop opposes the B-field of the magnet¾ opposing fields: repulsive force¾ this force opposes the gravitational force and slow down the magnet¾ cooling: resistance lowercurrent higher, B-field higher, opposing force strongerNSIBinducedBmagnetNSvmagnetcan be used to generate electric energy (and store it e.g. in a capacitor): demo: torch lightPHY232 - Remco Zegers Electromagnetic Inductions 17questionx x x xx x x xx x x xA rectangular loop moves in, and then out, of a constant magnet field pointing perpendicular (into the screen) to the loop. Upon entering the field (A), a …. current will go through