A point charge $\color{blue}{Q}$ is at the Origin of a Spherical Co-ordinate System. Find the $\color{blue}{\textsf{Flux}}$ which crosses the portion of a Spherical Shell described by $\color{green}{a \le \theta \le \beta}$ ??

Question

A point charge $\color{blue}{Q}$ is at the Origin of a Spherical Co-ordinate System. Find the $\color{blue}{\textsf{Flux}}$ which crosses the portion of a Spherical Shell described by  $\color{green}{a \le \theta \le \beta}$ ??

perl · Answer

this is calculus 3, do you have the formulas to use?

anonymous · Answer

Using Gauss's Law,

$$\large Net \; \; Flux \; \; crossing \;  ( \psi_{net}) = Q_{enclosed}$$

anonymous · Answer

@aum ..

aum · Answer

Assume a sphere of radius 'r' enclosing the point charge Q at its center.  Net flux crossing the sphere $\large \psi = Q.$  This flux passes through the entire surface area of the sphere, which is, $\large 4\pi r^2.  $  The flux passing through a portion of a sphere with surface area A will be: $\large \frac{A}{4\pi r^2} * Q.  $  We need to find A.

What is the surface area A of a portion of a sphere of radius 'r' bounded by $\alpha  \le \theta \le \beta$ and $0  \le \phi \le 2\pi$?

aum · Answer

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