Formula for electric field for capacitor and cylinder

[derek181]

My prof gave two formulas without much explanation as to where he got them from. For a parallel plate capacitor he gave it as E=k2∏q/A and for a cylinder he gave E=kq2/Lr where L is the length of the cylinder and r is the radius and A is the area. Can someone please explain how he derived these.

 

[tiny-tim]

hi derek181!

he gets it from the electric displacement field, D, which is always equal to the surface charge density, ie charge/area …

D = q/A or D = q/2πrL ​

(and see here)