# Lenz's Law. Definition from the book:

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1 Lenz's Law Definiion from he book: The induced emf resuling from a changing magneic flux has a polariy ha leads o an induced curren whose direcion is such ha he induced magneic field opposes he original flux change. My definiion: The induced emf resuling from a changing magneic flux is such ha a curren is creaed in a conducing coil so ha he resuling field from his curren ries o preven he magneic flux wihin he coil from changing. If he flux hrough he coil decreases, he direcion of he curren is such ha he field produced by i will increase he flux hrough he coil. The curren is in he opposie direcion if he flux would increase.

2 Lenz's Law (2) conducing coil We originally have a flux of 5 from he exernal B field. The exernal B field changes such ha he flux is now 2. An emf is produced in he conducing loop such ha i produces a field which ries o increase he flux o he original value of 5. Exernal B field

3 Anoher Graphical Descripion of Lenz's Law The ligh red area is an area of consan magneic field. Ouside his area, here is no field. As he conducing loop moves in a region wih no field, here is no curren in he loop since he magneic flux hrough he loop is consan (zero). As he loop eners he region of consan field, he magneic flux hrough he loop changes so here is an induced curren in he loop wih a direcion such ha he magneic field from he curren is opposie o he exernal field. When he loop moves hrough he consan field, here is once again no induced curren since he change is flux is zero (however here is sill a non-zero flux). When he loop leaves he region of consan field, he flux hrough he loop once again changes and induces a curren in he opposie direcion o ha induced before.

4 Elecric Generaor v Recall ha a conducing bar moving hrough a magneic field is given by: Emf v v L Bsin where θ is he angle beween he velociy and he direcion of B. B

5 Elecric Generaor (2) v B As he coil roaes hrough he field, he perpendicular componen of he velociy for each side of he coil becomes larger and smaller. The maximum value is he angenial velociy of he coil and he minimum value is zero.

6 Elecric Generaor (3) As he coil roaes hrough he field, he emf is given by: Emf = 2 v L Bsin and if he coil has N urns, your emf is given by: Emf = N 2 v L Bsin Recall ha wih a roaing objec, you can relae he angenial velociy o he angular frequency using: v r and also recall ha: Looking a he radius of he coil (remember we need his for he angenial velociy) we find i is: r W 2 r Puing his all ogeher we find: Emf sin N B A sin W 2 N B L W 2 Emf Emf max sin

7 AC Elecriciy Emf (rms) = Max Emf 2 If we plo: Emf Emf max sin we find he plo on he lef.

8 Muual Inducance This is he erm which describes wha happens when a changing curren in one coil (which produces a magneic field inside ha coil - hink Lenz's Law) induces a magneic field in a second coil. There is no direc physical conac beween he wo coils. Only he magneic field connecs hem. We find: N s s M I p or, solving for M, M N s s I p

9 Muual Inducance N s s M I p Recall Faraday's law: Emf s N s s Emf s N s s Emf s M I p Finally: Emf s M I p

10 Transformers Ofen, we wish o power a device wih a volage oher han wha is available o us. One example is a elevision which requires abou 15,000 V o accelerae he elecrons o near he speed of ligh so he magneic ''Seering Field'' can change heir direcion appreciably. Unforunaely, we do no have a source of 15,000 V in each of our houses. A ransformer is used o eiher ''sep up'' a volage or ''sep down'' one.

11 Transformers The ''ransformer equaion'' is given by: V s N s V p N p A good ransformer is consruced such ha no energy is los in he volage ransformaion. Since power is energy per ime, his means: P p P s I p I s I p V p or V s I s V s V p This means if a ransformer increases he volage, i simulaneously decreases he curren.

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