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Lecture 18-1 Ways to Change Magnetic Flux Changing the magnitude of the field within a conducting loop (or coil). Changing the area of the loop (or coil) that lies within the magnetic field. Changing the relative orientation of the field and the loop. motor generator http://www.wvic.com/how-gen-works.htm

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Lecture 18-2 N 1.define the direction of ; can be any of the two normal direction, e.g. point to right 2.determine the sign of Φ. Here Φ>0 3.determine the sign of ∆Φ. Here ∆Φ >0 4.determine the sign of using faraday’s law. Here <0 5.RHR determines the positive direction for EMF If >0, current follow the direction of the curled fingers. If <0, current goes to the opposite direction of the curled fingers. How to use Faraday’s law to determine the induced current direction

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Lecture 18-3 Eddy Current The presence of eddy current in the object results in dissipation of electric energy that is derived from mechanical motion of the object. The dissipation of electric energy in turn causes the loss of mechanical energy of the object, i.e., the presence of the field damps motion of the object. A current induced in a solid conducting object, due to motion of the object in an external magnetic field.

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Lecture 18-4 Self-Inductance As current i through coil increases, magnetic flux through itself increases. This in turn induces counter EMF in the coil itself When current i is decreasing, EMF is induced again in the coil itself in such a way as to slow the decrease. Self-induction (if flux linked) Faraday’s Law: (henry)

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Lecture 18-5

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Lecture 18-6 Solenoid: Archetypical Inductor Current i flows through a long solenoid of radius r with N turns in length l For each turn For the solenoid or Inductance, like capacitance, only depends on geometry

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Lecture 18-7 Potential Difference Across Inductor VV ++ - I internal resistance Analogous to a battery An ideal inductor has r=0 All dissipative effects are to be included in the internal resistance (i.e., those of the iron core if any)

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Lecture 18-8 RL Circuits – Starting Current 2. Loop Rule: 3. Solve this differential equation τ=L/R is the inductive time constant 1.Switch to e at t=0 As the current tries to begin flowing, self-inductance induces back EMF, thus opposing the increase of I. + -

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Lecture 18-9 Starting Current through Inductor vs Charging Capacitor

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Lecture 18-10 R1R1 R2R2 L V Which of the following statement is correct after switch S is closed ? 1.At t = 0, the potential drop across the inductor is V; When t = ∞, the current through R 1 is V/R 1 2.At t = 0, the potential drop across the inductor is V; When t = ∞, the current through R 1 is V. 3.At t = 0, the potential drop across the inductor is 0; When t = ∞, the current through R 1 is V/(R 1 +R 2 ) 4.At t = 0, the potential drop across the inductor is V; When t = ∞, the current through R 1 is V/R 2 Warm-up S

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Lecture 18-11 Remove Battery after Steady I already exists in RL Circuits 3. Loop Rule: 4.Solve this differential equation I cannot instantly become zero! Self-induction like discharging a capacitor 1.Initially steady current I o is flowing: - + 2. Switch to f at t=0, causing back EMF to oppose the change.

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Lecture 18-12 Behavior of Inductors Increasing Current –Initially, the inductor behaves like a battery connected in reverse. –After a long time, the inductor behaves like a conducting wire. Decreasing Current –Initially, the inductor behaves like a reinforcement battery. –After a long time, the inductor behaves like a conducting wire.

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Lecture 18-13 Energy Stored By Inductor 1.Switch on at t=0 2. Loop Rule: 3. Multiply through by I As the current tries to begin flowing, self-inductance induces back EMF, thus opposing the increase of I. + - Rate at which battery is supplying energy Rate at which energy is dissipated by the resistor Rate at which energy is stored in inductor L

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Lecture 18-14 Where is the Energy Stored? Energy must be stored in the magnetic field! Energy stored by a capacitor is stored in its electric field Consider a long solenoid where area A length l So energy density of the magnetic field is (Energy density of the electric field)

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Lecture 18-15 Physics 241 –Quiz A The switch in this circuit is initially open for a long time, and then closed at t = 0. What is the magnitude of the voltage across the inductor just after the switch is closed? a)zero b) V c) R / L d) V / R e) 2V

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Lecture 18-16 Physics 241 –Quiz B The switch in this circuit is closed at t = 0. What is the magnitude of the voltage across the resistor a long time after the switch is closed? a)zero b) V c) R / L d) V / R e) 2V

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Lecture 18-17 Physics 241 –Quiz C The switch in this circuit has been open for a long time. Then the switch is closed at t = 0. What is the magnitude of the current through the resistor immediately after the switch is closed? a)zero b) V / L c) R / L d) V / R e) 2V / R

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