Question

Space vehicles traveling through Earth'sradiation belts can intercept a significant number of electrons.The resulting charge buildup can damage electronic components anddisrupt operations. Suppose a spherical metallic satellite0.5 m in diameter accumulates2.4 µC of charge in one orbitalrevolution.

(a) Find theresulting surface charge density.
C/m²
(b) Calculate the magnitude of the electric field just outside thesurface of the satellite, due to the surface charge.
N/C

I know A, can you show me how to do b?

Answer 1

So for A you should have got

   σ = charge / area = 2.4 x 10^-6 / 4π 0.25² = 3.056 x 10^-6 Coulomb/m²

For part B...   there are actually two differentways you could do it. You could claim that right outside the shell,if you are very very close to the sphere, it appears flat (muchlike being on the surface of the Earth... it appears flat!)

So the E field from a flat sheet of charge withdensity   σ    is just

   E = σ / ε_o =3.056 x 10^-6 / 8.85 x 10^-12 = 3.45 x 10⁵ N/C

The other way, which is more exact but gives the same answer,is to realize that Gauss' law tells us that a sphere of charge actsexactly the same as a point charge of equal magnitude located atthe center of the sphere. The E field from a point charge is

   E = ( 1 / 4πε_o ) q / r²        and youcan see that if you plug in values to this expression you get thesame answer (because our value of σ wasjust q / 4πr² )

Hope this helps...