A rocket is to be launched by NASA for providing maintenance support to international space
station. As we all know that the fuel cylinders of rocket are detached after all the fuel in them is
burnt in order to reduce the total mass of the rocket. There are 2 stages of the fuel detachment,
first two cylinders are to be detached while the rocket is still in stratosphere of the Earth while
the last one is to be detached once the rocket is out of Earth’s atmosphere. As the second cylinder
is detached, it enters into a decaying orbit and eventually enters into the Earth’s atmosphere.
While entering the stratosphere, due to immense speed of the cylinder and air friction, a static
charge is developed on the surface.
As we know that there is going to be no charge inside the cylinder as well as outside or beyond
the boundary of the cylinder. If the surface of the fuel cylinder lies somewhere between 1 and 2
meters, and the volumetric charge density for this space is said to be 4r mC/m3
(r : distance from
the center of the cylinder).
Similarly, the volumetric charge density inside the cylinder i.e. less than 1 m as well as beyond
the surface i.e. greater than 2 m is considered to be zero.
Being an engineer, you are required to perform an analysis on this cylinder before the launch in
order to get an idea about the flux density of the electric field due to charge on its surface while
re-entry in order to extrapolate if it satisfies the safety standards.
So, if “L” is the length of the fuel cylinder, you are required to
1. Calculate the total charge in the space covered by 0 < r < r1 across the whole length
where the value of r1 is in between 1 and 2 m.
2. Figure out the expression to assess the value of electric flux density at r1.
3. What will be the exact value of electric flux density at 0.4 m, 1.3 m, 1.9 m and 4.0 m from
the center of the cylinder?
4. Also, provide your critical analysis on the purpose of this problem, as to why is being asked
and what’s the significance of this analysis for the said space program? If the result of this
analysis is not up to standard, is it important enough that it can cause a delay in launch