PHY2049: Chapter 301SubjectsÎInduced emfFaraday’s law (law #3 of electricity and magnetism)Lenz’s lawMotional emfGeneratorÎInductors and InductanceÎRL circuitsÎMagnetic energyÎTransformersÎSection 30-6 (Induced Electric Field): read the book!Important concept. Needed in Chapters 32 & 33PHY2049: Chapter 302InductorsÎCome in many shapes and sizes. Most common are small solenoids and toroids. Used in electronic circuits.PHY2049: Chapter 303Self-induced emfÎWhat is it?If a current through a coil of wire changes, B produced by it changes. This causes magnetic flux in the coil to change, leading to induced emf — self-induced emf.Self-induced emf can destroy a poorly-designed current supply for an electromagnet. Also, never touch the cables carrying the current to an electromagnet. (See a demo later.) iBPHY2049: Chapter 304InductanceÎMeasure of the strength of self-induced emf with respect to current changeÎDefinition: Inductance L of a coil with a uniform radiusÎWhy is this a good definition? Faraday’s law: This is actually the general definition of L Negative sign means: self-induced emf opposes change in current (just Lenz’s law!)ÎUnits Wb/A = T m2/A = henry = H Inductors used in electronics: µH Large electromagnets in labs: HiΦNLB≡dtΦdNBε −=dtdiLLε −=PHY2049: Chapter 305CHECKPOINT 5ÎThe figure shows the direction of a self-induced emf of a coil. Which of the following can describe the current through the coil?(a) constant and rightward(b) constant and leftward(c) increasing and rightward(d) increasing and leftwardLentz’s lawPHY2049: Chapter 306ExampleÎ L of a long solenoid Definition Field produced by long solenoid To increase L: increase n (many turns/length), A (large cross section), l (long solenoid)Î Two units for µ0H/m and T m/AniµB0=AlnµL20=iΦNLB≡PHY2049: Chapter 307CHECKPOINT 6ÎThe three inductors are identical, as are all the resistors and batteries. When the switch is closed at t=0, which circuit has the largest current through the battery?(a) 1(b) 2(c) 3(d) 1 and 2(e) 1 and 3(1) (2) (3)If i through L jumps from 0 to a non-zero value at t=0, then di/dt=∞. emf produced by L would be ∞, which is unphysical. di/dt is finite and i=0.PHY2049: Chapter 308ÎThe same three circuits, with identical L, R, and batteries. Long time after the switch is closed, which circuit has the largest current through the battery?(a) 1(b) 2(c) 3(d) 1 and 2(e) 1 and 3(continued)At t→∞, di/dt=0. So emf produced by L is 0. Inductor is then just a piece of wire.(1) (2) (3)PHY2049: Chapter 309ÎReaching steady state takes timeSelf-induced emf of inductor opposes current change from 0Current takes time to reach full valueÎClose switch at t=0Initial current: i = 0Initial emf of L:ℇL=ℇof batteryÎAt t ∞Final current: i = ℇ/RFinal emf of L:ℇL= 0(since di/dt=0. L behaves just as piece of wire.)RL CircuitPHY2049: Chapter 3010ÎWhat happens in between? Use loop rule:E– i R – L di /dt = 0ÎSolve the differential equationÎGeneral solution is(Check and see!)K = −E /R (necessary to make i = 0 at t = 0)ÎCurrent i and self-induced emf of LCompare with q and i in RC circuit(continued)LLRidtdiε=+)//( RLtKeRiε−+=)//(||RLtLeiR εεε−=−=())//(1RLteRiε−−=PHY2049: Chapter 3011Current and V vs Time())//(1RLteRiε−−=self-induced emf of inductor)//(||RLteεεL−=t/(L/R)())//(1RLteV ε−−=across resistorPHY2049: Chapter 3012Question 8ÎConsider three circuits wired as shown, containing the same resistance R and battery but different inductance L. Which of the three graphs shows the potential difference VRacross the circuit with the smallest L, after the switch is closed? a b cPHY2049: Chapter 3013ÎThe three circuits have identical L, R, and batteries. Which circuit has the shortest time constant?(a) 1(b) 2(c) 3(d) 1 and 2(e) 1 and 3Time ConstantTo find tau for circuits 2 or 3, use loop rule to write a differential equation. No need to solve it.(1) (2) (3)PHY2049: Chapter 3014Îdi/dt = –∞ will cause εL= – L di/dt = ∞Sparks! Can electrocute you ☹ÎUse a make-before-break switch to provide a current pathLoop rule: – i R – L di /dt = 0SolveGeneral solution isK=ℇ/R to make i=ℇ/R at t=0RL Circuit 2 (Disconnect battery)0=+LRidtdi)//( RLtKei−=)//( RLteRiε−=)//( RLteiRV ε−==PHY2049: Chapter 3015Current and V vs Time)//( RLteV ε−=())//(1RLteRiε−−=)//( RLteV ε−=)//( RLteV ε−=)//( RLteRiε−=across resistort/(L/R)self-induced emf of
View Full Document