xaer04
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Homework Statement
"What is the flux through the hemispherical open surface of radius R? The uniform field has magnitude E. Hint: Don't use a messy integral!"
\mid \vec{E} \mid= E
radius = R
Homework Equations
Electric Flux over a surface (in general)
\Phi = \int \vec{E} \cdot \,dA = \int E \cdot \,dA \cos\theta
Surface area of a hemisphere
A = 2\pi r^2
The Attempt at a Solution
If it were a point charge at the center (the origin of the radius, R), all of the \cos \theta values would be 1, making this as simple as multiplication by the surface area. The only thing that comes to mind for this, however, is somehow integrating in terms of d\theta and using the angle values on both axes of the hemisphere:
\left( \frac{\pi}{2}, \frac{-\pi}{2}\right)
But i can't just stick an integral in there like that... can I? I'm really lost on this one...