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Faraday’s Law

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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.

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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.

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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.

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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.

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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

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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.

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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 ) = 0.0050 T m 2 = 0.0050 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)(-0.0050 Tm 2 ) / (0.20 s) E = -(200)(-0.0050 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

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