Question

2. Two pieces of space junk are floating together in the same orbit near a damaged satellite. Both are neutral spheres, with diameters of 50cm and 100cm. A storage battery on the satellite explodes, sending ions in all directions and contaminating the spheres, which acquire charges. The smaller one has a charge of -10°C and the larger carries +20°C. Their surfaces are initially 4.5m apart. (a) What is the electric field midway between the centers of the spheres? (b) What is the potential energy of the two-sphere system? (c) The spheres drift toward each other, of course. When their surfaces collide, what is the kinetic energy of the system?

Answer 1

+20 pС — 10 pС 25 cm E 50 cm + + то * * х. 4.5 m

Figure shows the space junks which are two charged spheres . Small sphere of diameter 50 cm has      charge -10 $\mu$ C and another sphere of diameter 100 cm has charge +100 $\mu$ C .

Surfaces of sphere are 4.5 m apart . Hence mid point O beween centres is at 2.625 m from centre of either sphere. Electric field at mid point O pointing towards the negative charged sphere is given as

.........................(1)

E = KX 20 x 10-6 2.625 x 2.625 + 10 x 10-6 2.625 x 2.625 N/C

where K = 1/(4$\pi$
to
) = 9 $\times$ 10⁹ N m² C^-2 is Coulomb's constant

By substituting K in eqn. (1) , we get ,   E = 3.918 $\times$ 10⁴ N/C

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Potential energy U is given as

$U = -K \times \frac{20 \times 10^{-6} \times 10 \times 10^{-6} }{5.25} = - 9\times 10^{9}\times \frac{200\times 10^{-12}}{5.25} = - 0.343 J$

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When two spheres collide on each other , by conservation of energy , kinetic energy of system will be equal to intial potential energy 0.343 J