# Amplitude of the induced voltage across the coil

If anyone can advise that would be great.

1. The plane of a 5 turn coil of 5mm² 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 = 5cm²
B = 10 mT

2. φ = N.B.A φ = 5×10×10^-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) = -N•d(B•A)/dt = -N•B•dA/dt = N•B•ω•A•sin(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 = 5×10×10^-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.

Last edited:

## Answers and Replies

berkeman
Mentor
If anyone can advise that would be great.

1. The plane of a 5 turn coil of 5mm² 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 = 5cm²
B = 10 mT

2. φ = N.B.A φ = 5×10×10^-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) = -N•d(B•A)/dt = -N•B•dA/dt = N•B•ω•A•sin(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 = 5×10×10^-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)...