Question

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 0.98 m in diameter accumulates 2.7 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.

Answer 1

Answer:

a)$\rho = 8.9\times 10^{-7}\ C/m^2$

b)E=101,166.9 N/C

Explanation:

Given that

Diameter ,d=0.98 m

Charge ,q=2.7μC

a)

Surface charge density(ρ)

          Surface charge density is the charge per unit surface area of sphere.

So

$\rho =\dfrac{q}{\pi d^2}\ C/m^2$

$\rho =\dfrac{2.7\times 10^{-6}}{\pi \times 0.98^2}\ C/m^2$

$\rho = 8.9\times 10^{-7}\ C/m^2$

b)

Electric field E

$E =\dfrac{\rho}{\varepsilon _o}\ N/C$

$E =\dfrac{8.9\times 10^{-7}}{8.85\times 10^{-12}}\ N/C$

E=101,166.9 N/C