Today’s agenda: Induced emf. You must understand how changing magnetic flux can induce an emf, and be able to determine the direction of the induced emf. Faraday’s Law. You must be able to use Faraday’s Law to calculate the emf induced in a circuit. Lenz’s Law. You must be able to use Lenz’s Law to determine the direction induced current, and therefore induced emf. Generators. You must understand how generators work, and use Faraday’s Law to calculate numerical values of parameters associated with generators. Back emf. You must be able to use Lenz’s law to explain back emf.

We can quantify the induced emf described qualitatively in the previous section of this lecture by using magnetic flux. Experimentally, if the flux through N loops of wire changes by d  B in a time dt, the induced emf is Faraday’s law of induction is one of the fundamental laws of electricity and magnetism. I wonder why the – sign… *Faraday’s Law of Magnetic Induction Your text, page 959 of the 14 th edition, shows how to determine the direction of the induced emf. Argh! Lenz’s Law, coming soon, is much easier. *Well, one expression of Faraday’s Law

This is another expression of Faraday’s Law: is the magnetic flux. Faraday’s Law of Magnetic Induction We’ll use this version in the next lecture. In the equation The fine print, put here for me to ponder, and not for students to worry about. A magnetic force does no work on a moving (or stationary) charged particle. Therefore the magnetic force cannot change a charged particle’s potential energy or electric potential. But electric fields can do work. This equation shows that a changing magnetic flux induces an electric field, which can change a charged particle’s potential energy. This induced electric field is responsible for induced emf. During this lecture, we are mostly going to examine how a changing magnetic flux induces emf, without concerning ourselves with the “middleman” induced electric field.

NS I v + - Example: move a magnet towards a coil of wire. N=5 turns A=0.002 m 2

Possible homework hint: if B varies but loop  B. Ways to induce an emf:  change B  change the area of the loop in the field Possible homework hint: for a circular loop, C=2  R, so A=  r 2 =  (C/2  ) 2 =C 2 /4 , so you can express d(BA)/dt in terms of dC/dt.

Possible Homework Hint. I The magnetic field is not uniform through the loop, so you can’t use BA to calculate the flux. Take an infinitesimally thin strip. Then the flux is d  = BdA strip. Integrate from a to b to get the flux through the strip. a b  changing current changes B through conducting loop BB Ways to induce an emf (continued):

 change the orientation of the loop in the field  =90  =45  =0 