Find the Electric Flux of a point charge, \"Q\", through a circular AREA of radi

Question

Find the Electric Flux of a point charge, "Q", through a circular AREA of radius "r" if the point change is a distance "B" along the perpendicular axis through the center of the circular area. the circular area is perpendicular to the plane of the "paper". Use polar coordinates of p and phi when integrating over the area Show on the diagram, the area unit vector, the direction of the E field, for a positive charge and the angle theta between the normal and the electric field Express the magnitude of the point charge E field at the distance "r" shown in terms of the polar coordinates p and phi and the distance "B" Express the in terms of the polar coordinates p and phi and the distance "B" Express the infinitesimal area in terms of the polar coordinates p and phi Write the integral equation of the solution Perform the integration to obtain A sphere of radius "R" surrounds a charge "Q" at its center as shown in the picture. Find the electric Flux through a circular cap of half angle theta Carefully explain your reasoning. Show the results of two problems on this page are equivalent

Explanation / Answer

6) from guass law we know that flux through enclosed surface = Q/epsilon

this comes from E = q/(4*pi*r^2)*(Epsilon)

and dot product dA = r^2 * (dpsi) where psi = solid angle steradian

So for full sphere solid angle = 4*pi steradians

for 2*pi radians, we have  4*pi steradians

So for 2(theta) radians we have 4*theta steradians

So Net flux = q*(theta)/ pi*(epsilon)

5)E = q/(4*pi*epsilon*(rho^2+b^2))

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