Electro-Magnetic Induction

Electro-Magnetic Induction © David Hoult 2009

Magnetic flux © David Hoult 2009

© David Hoult 2009

If the magnitude of the flux density is B then the magnitude of the magnetic flux (f) linked with the area A is defined to be © David Hoult 2009

If the magnitude of the flux density is B then the magnitude of the magnetic flux (f) linked with the area A is defined to be f= AB © David Hoult 2009

f= AB units of flux © David Hoult 2009

f= AB units of flux Tm2 © David Hoult 2009

f= AB units of flux Tm2 1 Tm2 = 1 Weber (Wb) © David Hoult 2009

Now, the magnitude of the component of the flux density perpendicular to the area is Bcosq © David Hoult 2009

Now, the magnitude of the component of the flux density perpendicular to the area is Bcosq so the magnetic flux (f) linked with the area is now f= ABcosq alternatively © David Hoult 2009

In practice, the area in question is usually surrounded by a conductor, often a coil of wire. © David Hoult 2009

In practice, the area in question is usually surrounded by a conductor, often a coil of wire. If the coil of wire has N turns, we define the flux linkage as follows © David Hoult 2009

In practice, the area in question is usually surrounded by a conductor, often a coil of wire. If the coil of wire has N turns, we define the flux linkage as follows Flux linkage = N f © David Hoult 2009

EMF induced in a conductor moving through a uniform magnetic field © David Hoult 2009

The wire moves distance Ds in time Dt. In this time, a charge Dq moves past any point in the wire. © David Hoult 2009

The wire moves distance Ds in time Dt. In this time, a charge Dq moves past any point in the wire. work done = FDs © David Hoult 2009

The wire moves distance Ds in time Dt. In this time, a charge Dq moves past any point in the wire. work done = FDs FDs work done per unit charge = Dq © David Hoult 2009

The wire moves distance Ds in time Dt. In this time, a charge Dq moves past any point in the wire. work done = FDs FDs work done per unit charge = Dq work done per unit charge is the induced emf © David Hoult 2009

If the wire moves at constant speed, the force F must be © David Hoult 2009

If the wire moves at constant speed, the force F must be equal but opposite to the force acting on it due to the current I, induced in it © David Hoult 2009

If the wire moves at constant speed, the force F must be equal but opposite to the force acting on it due to the current I, induced in it F = -ILB © David Hoult 2009

If the wire moves at constant speed, the force F must be equal but opposite to the force acting on it due to the current I, induced in it F = -ILB FDs E = Dq © David Hoult 2009

If the wire moves at constant speed, the force F must be equal but opposite to the force acting on it due to the current I, induced in it F = -ILB FDs E = Dq -ILBDs E = Dq © David Hoult 2009

I = © David Hoult 2009

Dq I = Dt © David Hoult 2009

Dq - (Dq/Dt)LBDs I = E = Dq Dt and © David Hoult 2009

Dq - (Dq/Dt)LBDs I = E = Dq Dt and Ds = Dt © David Hoult 2009

Dq - (Dq/Dt)LBDs I = E = Dq Dt and Ds = v Dt © David Hoult 2009

Dq - (Dq/Dt)LBDs I = E = Dq Dt and Ds = v Dt E = -BLv © David Hoult 2009

Lenz’s Law When e.m.i. occurs, any induced current will flow in such a direction as to oppose the change producing it © David Hoult 2009

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 © David Hoult 2009

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 © David Hoult 2009

Lenz’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 © David Hoult 2009

Lenz’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 © David Hoult 2009

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 © David Hoult 2009

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... © David Hoult 2009

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! © David Hoult 2009

Electro-Magnetic Induction