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 1.7 m in diameter accumulates 3.1 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) σ = 3.41*10⁻7C/m^2

(b) E = 38,530.1 N/C

Explanation:

(a) In order to calculate the resulting surface charge density, you use the following formula:

$\sigma=\frac{Q}{S}$     (1)

σ: surface charge density

Q: charge of the satellite = 3.1 µC = 3.1*10^-6C

S: surface area of the satellite

The satellite has a spherical form, then, the area of the surface is given by:

$S=4\pi r^2$     (2)

r: radius of the satellite = d/2 = 1.7m/2 = 0.85m

You replace the equation (2) into the equation (1) and solve for the surface charge density:

$\sigma=\frac{3.1*10^{-6}C}{4\pi (0.85m)^2}=3.41*10^{-7}\frac{C}{m^2}$

The surface charge density acquired by the satellite on one orbit is 3.41*10⁻7C/m^2

(b) The electric field just outside the surface is calculate d by using the following formula:

$E=k\frac{Q}{R^2}$      (3)

k: Coulomb's constant = 8.98*10^9 Nm^2/C^2

R: radius of the satellite = 0.85m

$E=(8.98*10^9Nm^2/C^2)\frac{3.1*10^{-6}C}{(0.85m)^2}=38530.1\frac{N}{C}$

The magnitude of the electric field just outside the sphere is 38,530.1 N/C