Question

As a space shuttle moves through the dilute ionized gas of Earth’s ionosphere, the shuttle’s potential is typically changed by -1.0 Vduring one revolution. Assuming the shuttle is a sphere of radius 10 m, estimate the amount of charge it collects.

Short answer

$q=-1.1\times {10}^{-9}C$

Step-by-step solution

Given

• The potential of the shuttle is -1.0 V.
• Radius of a shuttle is 10 m (Assuming shuttle is a sphere).

Understanding the concept

The electric potential V at the surface of a drop of charge q and radius R is given by $\mathrm{V}=\frac{\mathrm{q}}{4{\mathrm{\pi \epsilon }}_0\mathrm{R}}$we find the amount of charge collected by shuttle.

Calculate the amount of charge collected

The charge is,

$\begin{array}{rcl}q& =& 4\pi {\epsilon }_{0}RV\\ & =& \frac{\left(10m\right)\left(-1.0V\right)}{8.99\times {10}^{9}N·m^2/C^2}\\ & =& -1.1\times {10}^{-9}C\end{array}$

Hence,the amount of charge it collects is$\begin{array}{rcl}q& =& -1.1\times {10}^{-9}C\end{array}$