1. Induction -->Inductors
Back to Circuits for a bit ….
Induction - Fall 2006

2. What the heck are we doing?
Today
7:30 AM we had our problem review session
Continue on with Induction & Inductors
Watch those piling up WebAssigns!
Monday
More of the same,
Wednesday
EXAMINATION #3
After Holiday
Complete the remaining six chapters in the syllabus.
Induction - Fall 2006

3. The field at A & B are the same.
The loop is pushed into a region where the magnetic field is into the page. The motion creates an induced current in the loop which in turn produces a magnetic field at A and B.
The field at A & B are the same.
The field at A is stronger than the one at B
The field at B is stronger than the one at A.
None of these.
Induction - Fall 2006

4. Today we will consider a Coil
Induction - Fall 2006

5. We will base our discussion on Faraday’s Law
Lentz
Induction - Fall 2006

6. Consider the following:
There are N turns in the solenoid.
There is a current flowing in the direction shown.
The power supply is set to 20 volts and the resistor is 10 ohms.
The coil wire has negligible resistance.
Induction - Fall 2006

7. The steady state current (20 volts, 10 ohms) in the circuit is
2 amperes
Less than 2 amperes
More than 2 amperes
Need more info.
Induction - Fall 2006

8. The DIRECTION of the magnetic field in the coil isB
From A to B
From B to A
Not enough information is given.
Induction - Fall 2006

9. Back to the coil diagram …
Recall from the last discussion that the magnetic field in the coil is given by:
n = #turns per unit length
Coil is infinitely long
Sort of
Induction - Fall 2006

10. Back to the coil diagram …
The Flux through a single turn of the coil is BA or m0niA.
Now, let’s increase the applied voltage linearly at a rate of DV/Dt.
The current will change at a rate DI/Dt.
Induction - Fall 2006

11. Back to the coil diagram …
For the single coil (as Dt0) FARADAY Says:
Induction - Fall 2006

12. Looking into the coil from the end with the red arrow, the emf around the coil induced current will be B
In a clockwise direction
In a counterclockwise direction
Induction - Fall 2006

13. So … the induced emf B
Will create a current that will oppose the change in the current.
The induced emf will therefore oppose the applied voltage (also an emf) from the power supply.
Induction - Fall 2006

14. So for the single coil
Induction - Fall 2006

15. Definition of Inductance L
UNIT of Inductance = 1 henry = 1 T- m2/A
FB is the flux near the center of one of the coils
making the inductor
Induction - Fall 2006

16. An inductor in the form of a solenoid contains 420 turns, is 16
An inductor in the form of a solenoid contains 420 turns, is 16.0 cm in length, and has a cross-sectional area of 3.00 cm2. What uniform rate of decrease of current through the inductor induces an emf of 175 μV?
Induction - Fall 2006

17.
Induction - Fall 2006

18. Look at the following circuit:
Switch is open
NO current flows in the circuit.
All is at peace!
Let's close the switch....
Induction - Fall 2006

19. At the INSTANT that the switch is closed, the current through the resistor is:
Zero
E/R
Can’t tell
Induction - Fall 2006

20. Don’t care .. we will be out by then!
Three years after the switch is closed, the current through the resistor is:
E/R
Zero
Don’t care .. we will be out by then!
Induction - Fall 2006

21. Graph? IR E/R Probably looks something Like this. time 11-11-06
Induction - Fall 2006

22. Close the circuit…
After the circuit has been closed for a long time, the current settles down.
Since the current is constant, the flux through the coil is constant and there is no Emf.
Current is simply E/R (Ohm’s Law)
Induction - Fall 2006

23. Close the circuit…
When switch is first closed, current begins to flow rapidly.
The flux through the inductor changes rapidly.
An emf is created in the coil that opposes the increase in current.
The net potential difference across the resistor is the battery emf opposed by the emf of the coil.
Induction - Fall 2006

24. Looking at the math
Induction - Fall 2006

25. Just as we did with the capacitor, we can solve this equation and we get:
Induction - Fall 2006

26. The growth
Induction - Fall 2006

27. Death of the current:
Induction - Fall 2006

28. Graph
Induction - Fall 2006

29. Consider the Solenoid Again…
n turns per unit length
Induction - Fall 2006

30. Inductance & Geometry Depends only on geometry just like C and
is independent of current.
Induction - Fall 2006

31. Max Current Rate of increase = max emf VR=iR ~current 11-11-06
Induction - Fall 2006

32. Solve the loop equation.
Induction - Fall 2006

33. IMPORTANT QUESTION Switch closes. No emf Current flows for a while
It flows through R
Energy is conserved (i2R)
WHERE DOES THE ENERGY COME FROM??
Induction - Fall 2006

34. For an answer Return to the Big C
We move a charge dq from the (-) plate to the (+) one.
The (-) plate becomes more (-)
The (+) plate becomes more (+).
dW=Fd=dq x E x d +q -q
E=e0A/d
+dq
Induction - Fall 2006

35. The calc
The energy is in
the FIELD !!!
Induction - Fall 2006

36. What about POWER?? power to circuit power dissipated by resistor
Must be dWL/dt
Induction - Fall 2006

37. So
Energy
stored
in the
Capacitor
Induction - Fall 2006

38. WHERE is the energy?? l
Induction - Fall 2006

39. Remember the Inductor??
?????????????
Induction - Fall 2006

40. So …
Induction - Fall 2006

41. ENERGY IN THE FIELD TOO!
Induction - Fall 2006

42. IMPORTANT CONCLUSION
A region of space that contains either a magnetic or an electric field contains electromagnetic energy.
The energy density of either is proportional to the square of the field strength.
Induction - Fall 2006

43. END OF TOPIC
Induction - Fall 2006