Find Max Power from 60Hz 4000A Power Line w/ 200m Wire

[seang]

Homework Statement

A 60Hz, 4000A power line passes near your house. You have 200m of wire. The closest you can get to the wire is 20m. Find the maximum power you can extract from the power line. The graphic shows that the loop has to be rectangular with side lengths A and B.

Homework Equations

The Attempt at a Solution

I took the wire to be in the Z direction, and so A is in the r direction. The B field from the wire is.

$$B = \frac{\mu_0 I}{2 \pi r}$$

Flux Linkage through the loop:

$$\psi = \frac{\mu_0 I}{2 \pi} \int_{0}^{B} \int_{20}^{20 + A} 1/r drdz$$

...

$$= \frac{\mu_0*4000sin(377t)*b}{2 \pi} * ln(\frac{(20 + A)}{20})$$

then,

$$200 = 2a + 2b , b = 100-a$$

$$V = \frac {d\psi}{dt} = .3016cos(377t)*(100-A) * ln(\frac{20+A}{20}$$

I used MatLab to find that the maximum voltage occurs when A = 31.8 meters. The corresponding voltage is 19.909 Volts.

So this is as far as I've gotten. I need either the Z of the load or the current in the loop to find the power, right? Is the induced current related to the source current?

 

[seang]

Maybe I can make this easier, I think I just need to know how current on one loop induced a current on another, given that I don't know the resistance of the second loop.

I mean, In this example, I know that the current on the second loop will be 60Hz, but how can I find the magnitude?