- #1
doktorwho
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Homework Statement
A sphere of radius ##a## is non-uniformly charged on its surface with a charge whose surface density is ##ρ_s(φ)=ρ_{so}(cosφ)^2## where ##φ## is the angle measures from the z axis, (0≤φ≤π) and ##ρ_{s0}## is a constant. Determine the expression for the total charge distributed on the sphere.
Homework Equations
##dQ=ρ_sdS##
The Attempt at a Solution
I know I am supposed to find the small surface element on which to integrate but the surface charge density is given by the angle and how am i supposed to make the surface element be in angle form. I tried thinking like this: In a circle the element ##dL## that is the small part of the circumference is ##rdφ## but don't know how to use that on the sphere..
The solution should be ##Q=\frac{4π}{3}ρ_{s0}a^2##
The problem i have now is how to start. I have to find the surface element and i don't know how, can you help?