Calculating emf from angular velocity

[Masafi]

I had 2 questions:

1. My textbook derives that the equation from lenz's and faraday's law

emf = - d(N*flux)/dt
= B * dA/dT

where dA/dt = length * speed

However, why does the N value disappear in the new equation?

Also, this question is given after:

2. A metal propeller rotates in a verical plane with angular vel 85 rad per sec. The length of the propeller from tip to tip is 2.5m. Calculate emf generated between centre and tip of properller. The horizontal component of Earth's magnetic field is 22 x 10^(-6) T (micro Tesla)

The answer is 1.5 x 10^(-3) V. I don't get this.

I did emf = B * dA/dt

dA/dt = length * speed
= 1.25 * (1.25 * 85)

which gives emf = 2.9 x 10 ^ (-3) V

i.e. double the answer

 

[Doc Al]

I had 2 questions:

1. My textbook derives that the equation from lenz's and faraday's law

emf = - d(N*flux)/dt
= B * dA/dT

where dA/dt = length * speed

That last step is a special case where you have a wire sweeping out an area. Note that the wire moves at a single speed.

However, why does the N value disappear in the new equation?

Presumably there is a single moving wire sweeping out an area.

Also, this question is given after:

2. A metal propeller rotates in a verical plane with angular vel 85 rad per sec. The length of the propeller from tip to tip is 2.5m. Calculate emf generated between centre and tip of properller. The horizontal component of Earth's magnetic field is 22 x 10^(-6) T (micro Tesla)

The answer is 1.5 x 10^(-3) V. I don't get this.

I did emf = B * dA/dt

dA/dt = length * speed
= 1.25 * (1.25 * 85)

which gives emf = 2.9 x 10 ^ (-3) V

i.e. double the answer

You took the speed of the propeller as equal to the speed of the tip. But the speed varies from zero at the center to a maximum at the tip. (What's the average speed?)

 

[Masafi]

That last step is a special case where you have a wire sweeping out an area. Note that the wire moves at a single speed.


Presumably there is a single moving wire sweeping out an area.


You took the speed of the propeller as equal to the speed of the tip. But the speed varies from zero at the center to a maximum at the tip. (What's the average speed?)

Thanks a lot :)

 

[jsmith613]

I personally don't understand how this question is done.
If I look at the formula and then at the question there is nothing in common?

 

[jsmith613]

so we know v = wr = 85 * 1.25 = 106.25 m/s
swept area = length * speed = 1.25 * 106.25 = 132.8

emf = (B*A*n)/t
emf = (132.8)/t
... how do I contnue (is this correct?)