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Let us construct a cylinder as shown in the figure, with R (radius of hemisphere) is the radius of the cylinder and 2R is its length. Now you can see that the charge q will be at the center of the cylinder.
Let
S1 = end surface of the cylinder, φ1 = flux through S1
S2 = half of the curved surface of the cylinder, φ2 = flux through S2
S = is the curved surface of the hemisphere and φ = flux through S
Since flux through the central plane is zero, by symmetry we have φ! + φ2 = q/2εo
We can also see that φ = φ2 = (q/2εo) – φ1
Since the surface subtends a plane angle of 90o at the q, the corresponding solid angle can be calculated using the formula , where α is the plane angle subtended.
Thus φ1 can be calculated as
Finally the required value
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