What does it mean for a charge to be uniformly distributed on a spherical shell?

[izzmach]

Surface current density, K is defined as:
K = σv
where σ is surface charge density and v is velocity.

Given a uniformly charged spherical shell with radius R, spinning at constant angular velocity ω, find the current.

So, I start with this formula:
dI = K dl
dI = σ Rω dl
and I placed the spherical shell at cartesian coordinate with its center at origin and try to solve the question in spherical coordinate.

What path should I take to express dl? Professor explained, dl = R dθ. What I don't understand is, why do we have to take R? Why not R sin(θ)?

 

[PeroK]

Surface current density, K is defined as:
K = σv
where σ is surface charge density and v is velocity.

Given a uniformly charged spherical shell with radius R, spinning at constant angular velocity ω, find the current.

So, I start with this formula:
dI = K dl
dI = σ Rω dl
and I placed the spherical shell at cartesian coordinate with its center at origin and try to solve the question in spherical coordinate.

What path should I take to express dl? Professor explained, dl = R dθ. What I don't understand is, why do we have to take R? Why not R sin(θ)?

What might "uniformly" charged mean in this case? Imagine you had 10 wires wrapped round the upper hemisphere. You could do that "uniformly" in two different ways.