The satellite is orbiting a star (radius of 700,000 kilometers) which has a huge

Question

The satellite is orbiting a star (radius of 700,000 kilometers) which has a huge net negative charge of 6 x 10^6 C (surface charge). You did not know the fact and launched a satellite (100 kilograms) on an orbit around the star (circular orbit, with a radius of 100 million kilometers). The satellite has an extra (positive) charge of 1000 C. The new attraction force was not foreseen previously, and you must compensate it somehow, because otherwise the satellite will fall into the star.

Somebody proposes neutralizing the satellite with a neighboring cosmic cloud, consisting of negatively charged ions (simple ionization, not double, so one extra negative charge per ion), having a density of 10^12 ions per cubic meter. The hull of the ship can be set up so that when it collides with an ion, it will absorb it. The plan is to absorb some negative charge (exactly 1000 C) from the cloud, and then transmit it to the probe with a wire from the ship, in order to make it electrically neutral. The spaceship is spherical with a hull of 150 m external radius, and 3 m thick, made of steel. Steel can be considered iron. Ship contains 1000 tons of water and an additional 1000 tons of people and supplies.

B) What distance must the ship travel through the cloud in order to acquire the desired negative charge?

After the ship had obtained the negative charge, a very thin conducting wire will be extended towards the satellite, in order to perform neutralization. The ship cannot be closer than 1 million kilometers from the satellite; so this will be the length of the thin wire.

The wire is being extended. When it reaches half distance, the sensors report that it generates, at a distance of 50,000 km in the direction of the extension (towards the satellite), a field of 5000 V/m. It is considered that the wire is charged now with a uniform linear charge.

C) What is the linear density of the charge on the wire at this moment?

Explanation / Answer

B)let V be the potential difference between the cloud and spaceship

let E be the electric field between them

we know that

V = E x d

where d is the distance

or d = (V/E)

C)lamda = (q/L)

where q = 1000 C and L = 50,000 x 10^3 m

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