Space vehicles traveling through Earth's radiation belts can intercept a significant number of electrons. The resulting charge buildup can damage electronic components and disrupt operations. Suppose a spherical metallic satellite 1.9 m in diameter accumulates 1.9 µC of charge in one orbital revolution. (a) Find the resulting surface charge density. (b) Calculate the magnitude of the electric field just outside the surface of the satellite, due to the surface charge.

a) 0.167 μC/m^2

b) 1.887 * 10^4 V/m

Explanation:

Hello!

First let's find the surface charge density:

a)

Since thesatellite is metallic, the accumalted charge will be uniformly distribuited on its surface. Therefore the charge density σ will be:

σ = Q/A

Where A is the area of the satellite, which is:

A=4πr^2 = πd^2 = π (1.9m) ^2

Therefore:

σ = (1.9) / (π (1.9) ^2) μC/m^2 = 0.167 μC/m^2

Now let's calculate the electric field

b)

Just outside the surface of the satellite the elctric field will be:

E = σ/ε0

Where ε0=8.85*10^-12 C/Vm

Therefore:

E = (0.167*10^-6 C/m^2) / (8.85*10^-12 C/Vm) = 0.01887 * 10^6 V/m

E = 1.887 * 10^4 V/m