E = -dV/dr = - w g which is constant
so at any r find the charge inside from Gauss
E * (4/3)pi r^2 = Q/eo
Q = (4/3) pi r^2 eo E
so
Q(r) = -w g (4/3) pi eo r^2
Q(r+dr) = - w g (4/3) pi eo (r^2+2 r dr + dr^2)
so charge between spheres =
Q(r+dr)-Q(r) = -w g (4/3) pi eo (2 r dr + dr^2)
as dr^2 is << r dr as dr -->0
Q(r+dr) - Q(r) =- w g (4/3) pi eo (2 r dr)
volume between = area of sphere * dr = (4/3) pi r^2 dr
so charge density between = - 2 w g eo /r
In a spherical region, the voltage is measured to be spherically symmetrical, with V = VCr) = wrg • The constants, wand g, are positive.
a.
Find the radial electric field.
b.
Use Gauss' Law to find the charge enclosed in a sphere of radius r.
c.
Find the charge enclosed by a sphere ofradius r+dr.
d.
Find the differential charge enclosed in the annular region between two
concentric spheres of radii rand r+dr.
e.
Find the differential volume ofthe annular region between two concentric
spheres of radii rand r+dr.
f.
Find the charge density, p = per) =?
2 answers
thank you very much Damon...you help me alot. thanks