An electrostatic system consists of two earthed concentric spherical shells of very small thickness and of radii "a" and "2a" respectively. The region a ≤ r ≤ 2a bears a charge distribution:

1. Determine a value for if the total charge is Q.

2. Show that the potential is:

Given that the laplacian of the electric potential for spherical symmetric coordinates is =

3. Sketch the directed electric field configuration of the system.

Neptune is the eighth planet from the sun. it was the first planet to get its existence predicted by  mathematical calculations  before it was actually seen through a telescope on sept. 23, 1846. irregularities in the orbit of  uranus  led french astronomer alexis bouvard to suggest that the gravitational pull from another celestial body might be responsible. german astronomer johann galle then relied on subsequent calculations to   spot neptune via telescope. previously, astronomer galileo galilei sketched the planet, but he mistook it for a star due to its slow motion. in accordance with all the other planets seen in the sky, this new world was given a name from greek and roman mythology — neptune, the roman god of the sea.