Problems of E-field of a Continuous Charge Distribution

[mysci]

dE = k_e(dq/r²)
How to change to complicated equation in the following picture?

 

[haruspex]

dE = k_e(dq/r²)
How to change to complicated equation in the following picture?

See http://www.physics.udel.edu/~watson/phys208/exercises/kevan/efield1.html, section on field from disk.

 

[mysci]

See http://www.physics.udel.edu/~watson/phys208/exercises/kevan/efield1.html, section on field from disk.

σ=Q/ πR² and
ρ=Q/ V
Then ρ=Q/ (πR² x dz) in here?

 

[haruspex]

σ=Q/ πR² and
ρ=Q/ V
Then ρ=Q/ (πR² x dz) in here?

Looks right.

 

[mysci]

Looks right.

In fact, I don't understand although I can deduce it.
The volume of sphere is (4/3)πR³, (πR2 x dz) = base area x height = volume of cylinder
Whether I got wrong about the picture is talking about the cylinder not sphere?

Thanks.

 

[haruspex]

In fact, I don't understand although I can deduce it.
The volume of sphere is (4/3)πR³, (πR2 x dz) = base area x height = volume of cylinder
Whether I got wrong about the picture is talking about the cylinder not sphere?

Thanks.

dz indicates an arbitrarily thin slice. Such a thin slice of a sphere is effectively a very short cylinder. This is the basis of calculus.