E field of a hemisperical shell

[nosmas]

My teacher explained a problem of a hemispherical shell in class but i don't understand what he is doing.

http://img116.imageshack.us/img116/7656/naamloos27mf.gif

 

[tiny-tim]

welcome to pf!

hi nosmas! welcome to pf!

(he only worked out the z component, because from symmetry the x and y components must be zero)

he sliced the shell into rings because for any one ring, the z component of the field must be the same …

so if the total charge of that ring is q, then it has the same effect (on the z component) as a charge q all at one point (instead of spread out around the ring)

then he multiplied charge x 1/distance² x cosθ
​

(he seems to have unnecessarily put in a lot of r's that then canceled …

i expect that's because they were in Eq 23-10)

 

[nosmas]

Equation 23-10 is dE = k*(dQ/r^2)

What I am struggeling with is how the distance to the point of interest z = rcos(theta) and how they came up with the charge on the ring?

 

[tiny-tim]

hi nosmas!

What I am struggeling with is how the distance to the point of interest z = rcos(theta) and how they came up with the charge on the ring?

rcosθ is the distance from the centre to the plane of the ring

the charge is the charge density times the area,

and the area is the arc-length (rdθ) times the circumference of the ring (2πrsinθ)