Unit 8: Electromagnetic Induction

Transcription

1 Unit 8: Electromagnetic nduction Electromagnetic induction phenomena. Faraday s law and enz s law. Examples of Faraday s and enz s laws. Mutual inductance and self-inductance. Stored energy on an inductor. Michael Faraday Hall of Royal Society ondon. Today

2 Electromagnetic induction phenomena Electromagnetic induction phenomena are known from 1830 when Michael Faraday and Joseph Henry discovered that a varying magnetic field produces electric currents on a coil (or a loop). Moving a magnet into a coil produces an electric current on coil Current 0 We ll see that a varying magnetic field isn t the only way to induce a current. Most important are changes on magnetic flux Tipler, chapter 28, ntroduction

3 Faraday s law nduced currents on a loop are due to electromotive forces depending on speed of change of magnetic flux passing throug the surface enclosed by the loop: ε = dφ Faraday s law Experimental law f R is the resistance of loop, a current will flow through the loop: i= ε R Derivative of flux against time give us the modulus of induced electromotive force, but not the polarity. The polarity of emf comes from enz s law. Tipler, chapter 28.2

4 Why could magnetic flux change? As magnetic flux through a loop surface comes from: φ = S r r BdS = S B ds Changes on flux can be due to: a) Changes on magnetic field, B b) Changes on surface of loop, S cos c) Changes on angle between B and S, ϕ ϕ Tipler, chapter 28.2

5 Why could magnetic flux change? a) Changes on magnetic field, B N S 0 induced

6 Why could magnetic flux change? b) Changes on surface of loop, S i r v produces a magnetic field through loop. When side of loop moves (speed v), magnetic flux changes and i appears.

7 Why could magnetic flux change? c) Changes on angle between B and S, ϕ A.C. Generator S r ϕ B v

8 enz s law Polarity of induced emf (ε) and intensity of current are always opposites to changes produced on magnetic flux through loop. t s very important to note that induced current is not opposite to flux, but to changes on flux. nduced current always tries to keep existing flux. Tipler, chapter 28.3

9 Examples. Applications of induced currents Generating an alternating current S r ϕ B v Eddy currents (Foucault currents) Data reading/writing head Tipler, chapter 28.5

10 Mutual nductance f we have two different and close loops (or circuits) electric current along one of circuits ( 1 ) creates a magnetic field and a magnetic flux through the second circuit (φ 21 ). The rate of φ 21 to 1 is the mutual inductance coefficient between circuits 1 and 2 (M 21 ): φ21 M 21 = φ21 = M B 1 due to B 1 Tipler, chapter 28.6

11 Mutual nductance n the same way could be defined M = φ 2 B 2 B due to 2 t can be proved that M 12 =M 21 =M M is mutual inductance between circuits 1 and 2. M Symbol of mutual inductance nductance unit: Henry (H) 1 Henry=1Wb/1A Tipler, chapter 28.6

12 Self-nductance f we have only one loop or circuit (instead two) the rate of magnetic flux to the intensity is the self-inductance of such circuit. The devices having a high self-inductance are the coils, solenoids or inductors. On a coil with a current, such current produces a magnetic field and a magnetic flux through coil. Rate of flux to is called self-inductance of coil, : φ B φ = φ = On circuits it s drawn with symbol: Physical device is called nductor Tipler, chapter 28.6

13 Example: Self-nductance of a solenoid A solenoid with a current, produces a magnetic field inside solenoid: B = µ 0 N l l N: turns Assuming B is uniform inside solenoid, magnetic flux through solenoid will be: µ N N NBA N 0 µ φ = = A = 0 l l 2 φ µ N A = 0 l Thus: 2 A A: cross section = Self-inductance of a solenoid Tipler, chapter 28.6

14 Electromotive force on an self-inductance. f a inductor is flowed by a varying current, an electromotive force appears: ε= dφ ε = d Polarity of induced e.m.f.: d d > 0 < ε = ε = d d

15 E.m.f. on a self-induction. Polarity n general, induced e.m.f is: d Term must take its own sign, being the positive terminal that where current is entering by on inductor: + ε= ε= d f current isn t varying (as on an D.C. circuit) there isn t induced e.m.f., and an inductor behaves as a short-circuit. d -

16 R circuit. Transient current ε + - d ε= t=0 R f switch is closed on t=0, a transient occurs and the loop Kirchoff s rule for this circuit is (for any time t): d R ε + = 0 The intensity of current flowing along the circuit will increase from 0 at time t=0 up tp reach the steady current. So, when d/=0, the electromotive force on terminals of inductor is zero and the inductor behaves as a shortcircuit. t theoretically will occur at time t= and the intensity will be =ε/r. t = 0 = 0 t = ε = R Tipler, chapter 28.7

17 Stored energy on an inductor ε + - d ε= R f we multiply the equation of this circuit by : R ε + x d = 0 ε = 2 R + d P g P R P Then, when intensity reachs its value, the stored energy on inductor is: W = d P = = d = 0 W = Stored energy on an inductor Tipler, chapter 28.7