What is the area element of angular distribution of charge?

[Kosta1234]

Homework Statement

Attempting to find a solution

Relevant Equations

$$ Q = \sigma ( \theta ) dA $$

I'm trying to get the Electric Field of a Thin spherical shell along $$ \hat z $$ axis.
In this problem I've got a charge/area density:

σ(θ)=σ0⋅cos(θ)σ(θ)=σ0⋅cos(θ)​

.

θ∈[0,π]θ∈[0,π]​

(theta is the polar angle)Can you please help me with how can I know the area element?
thanks.

 

[kuruman]

The spherical volume element of a sphere at radius $r$ is given by $dV=r^2~dr~\sin\theta~d\theta ~d\phi.$ An area element on the surface of that sphere is that divided by $dr$, namely $dA=r^2~\sin\theta~d\theta~ d\phi.$

More correctly, you should write $dQ=\sigma(\theta)dA$ for an element of charge on the surface. Then the total charge on the surface will be $Q=\int σ(θ)dA$.

 

[Kosta1234]

Thanks.