Question

One of the space shuttle missions attempted to perform an experiment in orbit using a tethered satellite. The satellite was to be released and allowed to rise to a height of 20 kilometers above the shuttle. The tether was a 20-kilometer copper-core wire, thin and light, but extremely strong. The shuttle was in an orbit with speed 7,600 meters per second, which carried it through a region where the magnetic field of the Earth had a magnitude of 3.3 x 10^-5 tesla. For your calculations, assume that the experiment was completed successfully, that the wire is perpendicular to the magnetic field, and that the field is uniform. 

a. An emf is generated in the tether.

i. Which end of the tether is negative? 

ii. Calculate the magnitude of the emf generated.

To complete the circuit, electrons are sprayed from the object at the negative end of the tether into the ionosphere and other electrons come from the ionosphere to the object at the positive end. The electric field that was induced in the wire is directed away from the shuttle and causes the current to flow in that direction in the tether. 

b. If the resistance of the entire circuit is about 10,000 ohms, calculate the current that flows in the tether. 

c. A magnetic force acts on the wire as soon as the current begins to flow. 

i. Calculate the magnitude of the force. 

ii. State the direction of the force.

Answer 1

(a) i) Consider the wire as a tube full of charges and focus on a single charge in the tube. That single charge is moving to the right in a B field pointing into the page. Using the RHR, that charge is pushed up to the satellite so the shuttle side is negative.

ii) Induced emf is given by ε = BLv = (3.3x10^–5)(20000m)(7600) = 5016 V

(b) V = IR  5016 = I (10000)  I = 0.5016 A

(c) i) F_b = BIL = (3.3x10^–5) (0.5016)(20000) F_b = 0.331 N

ii) The current flows up, away from the shuttle as indicated. Using the RHR for the given I and B gives the force direction on the wire pointing left which is opposite of the shuttle's velocity.