Faraday’s Law

Area Change  The sliding bar creates an emf by changing the area in the magnetic field. Constant magnetic field  The potential was due to the time rate of change of area.

Field Change  An emf can also be generated by changing the magnetic field.  The time rate of change of the field through a fixed loop provides the potential.

Field Orientation  The emf depends on the change in field or the change in area. Area perpendicular to the fieldArea perpendicular to the field  This suggests that the product of the field and area perpendicular matters.

Magnetic Flux  The product of the field and area perpendicular to the field is the magnetic flux.  The magnetic flux is measured in webers. 1 Wb = 1 T m 21 Wb = 1 T m 2  The magnetic field can be thought of as a flux density.

Faraday’s Law  The flux can be used to get the induced emf. Sign indicates polaritySign indicates polarity  This is Faraday’s Law of induction.  For multiple turns the emf is multiplied. N turns of wireN turns of wire N  is the flux linkageN  is the flux linkage

Coil Flux  A circular flat coil has 200 turns of wire with a total resistance of 25  and an enclosed area of 100 cm 2.  There is a perpendicular magnetic field of 0.50 T that is turned off in 200 ms.  Find the current induced in the coil.  This problem has three parts.  To get the current from the resistance the voltage is needed.  To get the voltage the flux is needed. Flux linkage works, too  Find the flux first.

Flux to Current  The magnetic flux is  = BA.  = (0.50 T)(100 cm 2 )  = (0.50 T)(100 cm 2 )  = (0.50 T)(0.010 m 2 )  = (0.50 T)(0.010 m 2 )  = T m 2  = T m 2  The change in flux is negative since it is turned off.  The induced emf is E =  N  /  t E =  N  /  t E = -(200)( Tm 2 ) / (0.20 s) E = -(200)( Tm 2 ) / (0.20 s) E =  V = 5.0 V E =  V = 5.0 V  The induced current comes from Ohm’s Law. I = V/R I = (5.0 V) / (25  ) I = 0.20 A next