Answer
34m.
Yes, this would be stealing.
Work Step by Step
The changing current in the overhead wire creates a sinusoidally varying magnetic field.
Approximate the field strength by using the average distance from the power line to the coil.
$$B_o=\frac{\mu_o I}{2\pi r_{average}}$$
Approximate the change in flux as the maximum flux through the coil, as stated in the problem. The maximum flux is the field multiplied by the coil area.
$$\Delta \Phi=B_o(2.0m)(L)= \frac{\mu_o I}{2\pi r_{average}}(2.0m)(L)$$
The hint in the problem points out that the flux changes from its maximum to zero in one-quarter cycle.
Set the maximum emf equal to 170 V.
$$emf=170V=N\frac{\Delta \Phi}{\Delta t}=N\frac{\frac{\mu_o I}{2\pi r_{average}}(2.0m)(L)}{\Delta t}$$
Solve for the length L.
$$L= \frac{(emf)\Delta t}{N\frac{\mu_o I}{2\pi r_{average}}(2.0m)}$$
$$L= \frac{(170V)(1s/240)}{(2000)\frac{\mu_o (155A)}{2\pi 6.0m}(2.0m)}\approx 34m$$
Yes, this would be stealing. The current in the 2000-turn coil creates a back emf in the overhead wire. By conservation of energy, the energy to power the farm equipment comes at the expense of the power company.
