1. Electro-Magnetic Induction
© D Hoult 2008

2. The Laws of Electro-magnetic Induction

3. Lenz’s Law
When e.m.i. occurs, any induced current will flow in such a direction as to

4. Lenz’s Law
When e.m.i. occurs, any induced current will flow in such a direction as to oppose the change producing it

5. Lenz’s Law
When e.m.i. occurs, any induced current will flow in such a direction as to oppose the change producing it
It should be clear that Lenz’s law is an “electro-magnetic version” of

6. Lenz’s Law
When e.m.i. occurs, any induced current will flow in such a direction as to oppose the change producing it
It should be clear that Lenz’s law is an “electro-magnetic version” of the law of conservation of energy

7. Lenz’s Law Faraday’s Law
When e.m.i. occurs, any induced current will flow in such a direction as to oppose the change producing it
Faraday’s Law
The induced emf is directly proportional to the

8. Lenz’s Law Faraday’s Law
When e.m.i. occurs, any induced current will flow in such a direction as to oppose the change producing it
Faraday’s Law
The induced emf is directly proportional to the rate of change of flux linking the conductor

9. The sense of the induced current can be predicted using Fleming’s RIGHT hand rule

10. The sense of the induced current can be predicted using Fleming’s RIGHT hand rule
which is pretty much like Fleming’s left hand rule

11. The sense of the induced current can be predicted using Fleming’s RIGHT hand rule
which is pretty much like Fleming’s left hand rule
except, guess what...

12. The sense of the induced current can be predicted using Fleming’s RIGHT hand rule
which is pretty much like Fleming’s left hand rule
except, guess what... using the right hand instead of the left hand !

13. ThuMb
Motion
First finger
Field
SeCond finger
Current

14. Both the laws of e.m.i. can be combined in a single mathematical statement

15. Both the laws of e.m.i. can be combined in a single mathematical statement
Faraday

16. Both the laws of e.m.i. can be combined in a single mathematical statement
Faraday Df
E a Dt

17. Both the laws of e.m.i. can be combined in a single mathematical statement
Faraday Df
E a Dt
Faraday + Lenz

18. Both the laws of e.m.i. can be combined in a single mathematical statement
Faraday Df
E a Dt
Faraday + Lenz Df
E a - Dt

19. Using the S.I. system of units the constant of proportionality is 1 so, if (as is often the case) the conductor is a coil of wire having N turns, we have

20. Using the S.I. system of units the constant of proportionality is 1 so, if (as is often the case) the conductor is a coil of wire having N turns, we have Df
E = -N Dt

21. Using the S.I. system of units the constant of proportionality is 1 so, if (as is often the case) the conductor is a coil of wire having N turns, we have Df
E = -N Dt
This equation is often referred to as Neumann’s Law

22. For a wire moving at 90° to a field with speed v, the induced emf is given by

23. For a wire moving at 90° to a field with speed v, the induced emf is given by E = - B L v

24. E = - B L v

25. Ds
E = - B L v = - B L Dt

26. Ds DA
E = - B L v = - B L
= - B Dt Dt

27. Ds DA Df
E = - B L v = - B L
= - B
= - Dt Dt Dt

28. Ds DA Df
E = - B L v = - B L
= - B
= - Dt Dt Dt
This suggests that change of flux linking a conductor and flux cutting by a conductor are equivalent actions