In one of NASA's space tether experiments, a 20.0 km-long conducting wire was deployed by the space shuttle as it orbited at 7.86 ✕ 103 m/s around Earth and across Earth's magnetic field lines. The resulting motional emf was used as a power source. If the component of Earth's magnetic field perpendicular to the tether was 1.38 ✕ 10−5 T, determine the maximum possible potential difference (in V) between the two ends of the tether.

Respuesta :

Explanation:

It is given that,

Length of wire, l = 20 km = 20,000 m

Velocity around earth, [tex]v=7.86\times 10^3\ m/s[/tex]

Earth's magnetic field, [tex]B=1.38\times 10^{-5}\ T[/tex]

Motional EMF is given by :

[tex]\epsilon=Blv\ sin\theta[/tex]

Where, [tex]\theta=90[/tex]

[tex]\epsilon=1.38\times 10^{-5}\times 20000\ \times 7.86\times 10^3\ sin(90)[/tex]

[tex]\epsilon=1939.4\ V[/tex]

So, the maximum possible potential difference (in V) between the two ends of the tether is 1939.4 V. Hence, this is the required solution.

The maximum possible potential difference (in V) between the two ends of the tether will be [tex]e=1939.4V[/tex]

What will be the maximum possible potential difference (in V) between the two ends of the tether?

It is given that

Length of the wire L= 20km=20000m

Velocity around the earth = [tex]7.86\times10^{3}\ \frac{m}{s}[/tex]

Earths magnetic [tex]1.38\times10^{-5}T[/tex]

The EMF will be given as

[tex]e=BLVsin\theta[/tex]

[tex]\theta=90[/tex]

put the values

[tex]e=1.38\times10^{-5}\times20000\times7.86\times10^3 sin(90)[/tex]

[tex]e=19.39.4V[/tex]

Thus the maximum possible potential difference (in V) between the two ends of the tether will be [tex]e=1939.4V[/tex]

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