Abeam contains 1.1 × 105 doubly charged positive ions per cubic centimeter, all of which are moving north with a speed of 1.5 × 105 m/s. what is (a) the magnitude of the current density and (b) direction of the current density . (c) what additional quantity do you need to calculate the total current i in this ion beam?

(a) The beam contains  doubly charged positive ions per cubic centimeter. Each ion has a charge equal to 2 protons, so the total charge contained in 1 cubic centimeter is the number of ions times 2 times the charge of 1 proton:

1 cubic centimeter corresponds to , so the charge density is equal to


So now we can calculate the magnitude of the current density, which is given by


(b) Since the charges are positive, then the direction of the current density is equal to the direction of the velocity v.

(c) The current density is also equal to the ratio between the current I and the cross-sectional area A:

So, in order to find the current I, we also need the cross-sectional area A of the beam.

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.