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Amplitude of the induced voltage across the coil

by lee.perrin@gm
Tags: induced voltage, inductance, magnetic field
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lee.perrin@gm
#1
Mar30-10, 10:02 PM
P: 8
If anyone can advise that would be great.

1. The plane of a 5 turn coil of 5mm cross sectional area is rotating a 1200 r.p.m in a magnetic field of 10mT.

Q. Calculate the amplitude of the induced voltage across the coil

Data:

5 turns
c = 1200 rpm
A = 5cm
B = 10 mT

2. φ = N.B.A φ = 51010^-3 5 10^-2
φ = 2.5 10^-3

V = dφ/dt or N.A. dB/dt

The equation thought to have been used is the following but the Length is not vissible to me.

V/L = c x B c being the speed
B field
L lenth of wire

3. I have tried two avenues please advise

a: V(t) = -Nd(BA)/dt = -NBdA/dt = NBωAsin(ωt)
V(t) =(5)(10x10^-3)(125.66370599999999)(5)sin(ωt) = 31.415 sin(ωt) volts.

Or

b: And using the following, saying t = 60 sec

Then φ = N.B.A φ = 51010^-3 5 10^-2
φ = 2.5 10^-3

And V = dφ/dt or N.A. dB/dt = 4.17x10^-3 V

My concern here is that 1200rpm was not used.
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berkeman
#2
Apr2-10, 05:28 PM
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P: 40,947
Quote Quote by lee.perrin@gm View Post
If anyone can advise that would be great.

1. The plane of a 5 turn coil of 5mm cross sectional area is rotating a 1200 r.p.m in a magnetic field of 10mT.

Q. Calculate the amplitude of the induced voltage across the coil

Data:

5 turns
c = 1200 rpm
A = 5cm
B = 10 mT

2. φ = N.B.A φ = 51010^-3 5 10^-2
φ = 2.5 10^-3

V = dφ/dt or N.A. dB/dt

The equation thought to have been used is the following but the Length is not vissible to me.

V/L = c x B c being the speed
B field
L lenth of wire

3. I have tried two avenues please advise

a: V(t) = -Nd(BA)/dt = -NBdA/dt = NBωAsin(ωt)
V(t) =(5)(10x10^-3)(125.66370599999999)(5)sin(ωt) = 31.415 sin(ωt) volts.

Or

b: And using the following, saying t = 60 sec

Then φ = N.B.A φ = 51010^-3 5 10^-2
φ = 2.5 10^-3

And V = dφ/dt or N.A. dB/dt = 4.17x10^-3 V

My concern here is that 1200rpm was not used.
You should write out the function φ(t) (hint: it is a sinusoidal function), then differentiate it to find V(t)...


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