Question

The flying wallendas decided to tale their high wire, tight rope walking acrobatic circus act to the next level. The idea was to walk across the grand canyon on a single wire that was not actually attached to either end but instead levitated by a strong magnetic field. Tino (85kg), Nik (82kg), and Evita (65kg) Wallenda purchased a discarded high voltage line (1200kg) that was just long enough to cross the 69.5 meter East to West gap and was able to carry a maximum current of 1500 Amps. In need of your physics expertise they have asked you to calculate the magnitude and direction of the magnetic field necessary to levitate the wire as the three wallendas cross the Grand Canyon in their famous 3-person pyramid!! Calculate carefully, their lives are in your hand.

Answer 1

First, calculate the force of gravity which the electromagnetic (or Ampere's) force should overcome:

$$F=g(M_\text{rope}+m_\text{Nik}+m_\text{Tino}+m_\text{Evita}).$$

Second, the Ampere's force must act upward and have the same magnitude:

$$F=IBL=1500\cdot B\cdot69.5,$$

find $B$:

$$B=\frac{g(M_\text{rope}+m_\text{Nik}+m_\text{Tino}+m_\text{Evita})}{IL}=\frac{14033.6}{1500\cdot69.5}=0.135\text{ T}.$$

According to the right-hand rule, the magnetic field must be directed from right to the left if the current in the rope flows along the wire into the screen.