Question

what is the electric field at the centre (γ 2 , that carries a uniform volumetric charge density ,-аф(mg)? (The charges are distributed in this hemispherical 3D space. Use spherical coordinates due to the hemispherical geometry.) 1, 0) of a hemisphere bounded by r-a, 0 < θ < π/2 and 0 < φ <

The problem must be solved with this formula we were able to define all the values in this formula except the r' vector which we are unable to get

The r=0 given in the Q

the dv'= (r^2)sin(theta) dr dtheta dphi

pv(r')= 3phi given in the question  

Note that the r' vector is a vector from the origin to the differential volume element and the r vector is from the origin to the observation point. Some texbooks define these 2 vectors as one R vector which is why in the formula it says r-r' whenever they are used

Answer 1

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