Elecromagnetic Induction
1 Electromagnetic Induction: Faraday's Law
OBJECTIVE: To understand how changing magnetic fields can produce electric currents. To examine Lenz's Law and the derivative form of Faraday's Law. EQUIPMENT: Circular Coils apparatus, PC sound card, FFTScope, magnet , paper clip, cables, small (magnetic) compass, paper clip, multimeter w/long cable INTRODUCTION: Have you ever wondered how a telephone works? You may recall (perhaps in middle school or high school) that sound waves from your voice are converted to electricity by the microphone and that electricity is converted back to sound waves by the speaker, but how does that actually happen? Such inventions as the telephone, electric generators, electric guitar pickups, electrical transformers, car cruise controls, induction stoves and blood flow meters all exploit the fact that a changing magnetic field can give rise to an electrical current, a phenomenon we call electromagnetic induction. The mathematical law that relates the changing magnetic field to the induced current (or, more accurately, the induced voltage or emf) is called
2 Faraday's Law, named after the man (among others) who first observed it in the laboratory around 1830. You may recall from lecture that magnetic flux through a surface in a magnetic field B is = ∫ B. n dA where
n
is a unit vector perpendicular to area element dA
note that if B is constant and the surface is a plane with area A, this reduces to =B Acos A conducting loop which has an ammeter attached to it will register a current if the magnetic flux through the loop changes in time. The change may arise from motion:
Or the change in flux may be due to the changing current in a circuit. In (a) below there is no induced emf in loop 2 but when the battery is connected, the increasing current in loop 1 produces a changing magnetic field and hence induces an emf in loop 2.
3
Faraday noted that the emf induced in a loop is proportional to the rate of change of magnetic flux
OBJECTIVE: To understand how changing magnetic fields can produce electric currents. To examine Lenz's Law and the derivative form of Faraday's Law. EQUIPMENT: Circular Coils apparatus, PC sound card, FFTScope, magnet , paper clip, cables, small (magnetic) compass, paper clip, multimeter w/long cable INTRODUCTION: Have you ever wondered how a telephone works? You may recall (perhaps in middle school or high school) that sound waves from your voice are converted to electricity by the microphone and that electricity is converted back to sound waves by the speaker, but how does that actually happen? Such inventions as the telephone, electric generators, electric guitar pickups, electrical transformers, car cruise controls, induction stoves and blood flow meters all exploit the fact that a changing magnetic field can give rise to an electrical current, a phenomenon we call electromagnetic induction. The mathematical law that relates the changing magnetic field to the induced current (or, more accurately, the induced voltage or emf) is called
2 Faraday's Law, named after the man (among others) who first observed it in the laboratory around 1830. You may recall from lecture that magnetic flux through a surface in a magnetic field B is = ∫ B. n dA where
n
is a unit vector perpendicular to area element dA
note that if B is constant and the surface is a plane with area A, this reduces to =B Acos A conducting loop which has an ammeter attached to it will register a current if the magnetic flux through the loop changes in time. The change may arise from motion:
Or the change in flux may be due to the changing current in a circuit. In (a) below there is no induced emf in loop 2 but when the battery is connected, the increasing current in loop 1 produces a changing magnetic field and hence induces an emf in loop 2.
3
Faraday noted that the emf induced in a loop is proportional to the rate of change of magnetic flux