By using Gauss' law, can the electric field be p/(pi*ε*r^2)

[adamaero]

Homework Statement

By using Gauss' law, can the electric field be p/(pi*ε*r^2) instead of p/(2*pi*ε*r) where "p" is the charge distribution?

Relevant Equations

Q = p*l

Which is better to use? The equation for the area or the circumference of a circle?

Schaum's Electromagnetics (4 ed) by Edminister
vs

http://hyperphysics.phy-astr.gsu.edu/hbase/electric/elecyl.html

 

[vela]

You should be able to figure out the answer to your question on your own. Do you know how to calculate flux?

 

[rude man]

You could also check dimensions, which every physics student should. Of course, that is not what is asked for here but you should nevertheless always do it.

 

[Orodruin]

Note that you must add both the flux through the end caps as well as that through the lateral area to get the total flux through a closed surface. However, the field is radial and therefore the flux theough the end caps is zero.

 

[archaic]

You should be able to figure out the answer to your question on your own. Do you know how to calculate flux?

The flux in the second way is easy, the first method, however, is somewhat ambiguous. It is suggesting that ##\rho=r/2##.

 

[mjc123]

The first method seems simply wrong; it assumes the surface area of a cylinder is πr²L, rather than 2πrL. The answer is dimensionally wrong.