Thank you for visiting In 1996 NASA conducted the Tethered Satellite Experiment During this experiment a wire 1 70 x 10 4 meters in length was deployed from the. This page is designed to guide you through key points and clear explanations related to the topic at hand. We aim to make your learning experience smooth, insightful, and informative. Dive in and discover the answers you're looking for!
Answer :
In this question, we're looking at the Tethered Satellite Experiment conducted by NASA, where the goal was to generate a motional electromotive force (EMF) using a wire.
Motional EMF: This is the EMF induced in a conductor moving through a magnetic field. The formula for calculating the motional EMF (ε) is given by:
[tex]ε = B \cdot v \cdot L \cdot \sin(θ)[/tex]
where:
- [tex]B[/tex] is the magnetic field strength (in teslas),
- [tex]v[/tex] is the velocity of the conductor (in meters per second),
- [tex]L[/tex] is the length of the conductor (in meters),
- [tex]θ[/tex] is the angle between the magnetic field and the direction of motion of the wire.
In this experiment:
- The length of the wire, [tex]L[/tex], is [tex]1.70 \times 10^4[/tex] meters.
- The speed of the shuttle, [tex]v[/tex], is [tex]8.87 \times 10^3[/tex] m/s.
- The Earth’s magnetic field, [tex]B[/tex], is [tex]6.43 \times 10^{-5}[/tex] T.
Since it is stated that the wire moved perpendicular to the Earth's magnetic field, the angle [tex]θ[/tex] is [tex]90^\circ[/tex], and [tex]\sin(90^\circ) = 1[/tex].
So the formula simplifies to:
[tex]ε = B \cdot v \cdot L[/tex]
Plug in the values:
[tex]ε = 6.43 \times 10^{-5} \times 8.87 \times 10^3 \times 1.70 \times 10^4[/tex]
Calculating this gives:
[tex]ε = 6.43 \times 8.87 \times 1.70 \times 10^2[/tex]
[tex]ε \approx 9.67 \times 10^3 \text{ volts}[/tex]
Thus, the motional EMF generated between the ends of the wire would be approximately [tex]9.67 \times 10^3[/tex] volts. This experiment highlights the principle that a moving wire in a magnetic field can generate electricity, illustrating a fundamental concept in electromagnetism.
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