12.1.1:
Emf is the amount of mechanical energy converted into electrical energy per unit charge. The unit of an induced emf is the volt. This happens when the free charges moving in a magnetic field are contained within a conductor. This is affected by the rate of flux cutting (Also just v for the velocity the conductor moves through the field), B - field of flux density and L, the length of the conductor itself. The optimal angle for a conductor to flux cut is perpendicular to the magnetic field lines.
12.1.2:
FB= FE
FB= BeV
E = -dV/dx = V/L
FE = Ee = Ve/L
Ve/L = BeV
V=BLV
12.1.3:
Faraday's law shows that the induced emf is equal to the rate of change of flux. This is due to the fact that the different variables, flux density, speed of movement and length of the conductor change at the rate which the conductor cuts through the magnetic field lines. This applies to all examples of induced emfs.
12.1.4:
This happens mainly during AC power production, where the power is sent primarily to the coil causing a change in the magnetic field in the transformer. Transformer-induced emf is induced by a time-changing magnetic flux, namely a wire in a magnetic field that changes with time.
12.1.5:
Faraday's: Total flux linkage is given by NФ. The rule governing induced emf can be stated as the magnitude of an induced emf being proportional to the rate of change of flux linkage. emf = N(ΔФ/Δt)
Lenz's: The direction of an induced emf opposes the change which caused it. For example if a current was induced downwards the force would be upwards. The original motion would be opposed.
Questions:
39.
a)
Emf = BLV
50x10^-6 x 0.2 x 20
= 2x10^-4 v
b)
R = 2
I=V/R
=2x10^-4/2
=1x10^-4 a
c)
I^2R
=2x10^-8 w
d)
2x10^-8 w
e)
20 meters in one second.
f)
w=fxd
f = w/d
f=2x10^-8 / 20 = 1x10^-9 N
40.
a)
AxB
2x10^-4 x 100 x 10^-6
=2x10^-8
=50x2x10^-8
=1x10^-6
b)
Since flux changed density to 50 then flux enclosed is 0.5x10^-6
ΔB/Δt = 1.0 – 0.5 / 2
=0.25 MTm^-2s^-1
c)
Induced emf = rate of change of flux = 0.25 MV
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