Electromagnetic Induction

 = BA  = BA cos  Magnetic flux: is defined as the product of the magnetic field B and the area A of the plane of the loop through which it passes. where θ is the angle between the direction of B and a line drawn perpendicular to the plane of the loop. If θ = 0˚ the flux is a maximum. Units: Tm 2 Weber (Wb)

A change in flux can occur in two ways: 1. By changing the magnetic field B going through a constant loop area A: ΔΦ = ΔB A

2. By changing the effective area A in a constant magnetic field B: ΔΦ = B ΔA

Faraday’s Law: "A magnetic flux changing at the rate of one weber per second will induce an emf of one volt for each turn of the conductor” ɛ = average induced emf (V) N = number of turns ΔΦ = change in magnetic flux (Wb) Δt = time interval (s) The minus sign indicates that the induced emf opposes the change in flux through the loop.

LENZ’S LAW: “An induced emf produces a current whose magnetic field always opposes the change in magnetic flux which caused it”

If the B field is increasing, the induced field acts in opposition to it. If the B field is decreasing, the induced field acts in the same direction of the applied field to try to keep it constant.

b. FLUX = INCREASING B secondary = UP

c. FLUX = DECREASING B secondary = DOWN

13.5 A coil of wire having an area of m 2 is placed in a region of constant flux density equal to 1.5 T. In a time interval of s, the flux density is reduced to 1 T. If the coil consists of 50 turns of wire, what is the induced emf? A = 1x10 -3 m 2 ΔB = ( ) = T Δt = s N = 50 turns ΔΦ = ΔB A = - 0.5(1x10 -3 ) = -5x10 -4 T.m 2 = -5x10 -4 Wb = - 25 V

13.6 A square coil consisting of 80 turns of wire and having an area of 0.05 m 2 is placed perpendicular to a field of flux density 0.8 T. The coil is flipped until its plane is parallel to the field in a time of 0.2 s. What is the average induced emf? A = 0.05 m 2 B = 0.8 T Δt = 0.2 s N = 80 turns ΔΦ = B A = 0.8(0.05) = 4x10 -2 Wb = - 16 V