Question

z A charged sphere of radus R (see picture below) has non unform density that is volume roportiomal to distance from its center O where b is a positive constant of proper units. (Consider values of R and b to be b) (18 pts) Find r and thickness dr)
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Answer #1

volume density=br

b=volume density/r

unit of b=coulomb/m^4 =C/m^4

let us take a small sphere at distance r of thickness dr

we got dq=volume density*4*pi*r^2dr=br*4*pi*r^2dr=4*pi*b*r^4dr

integrating we got

Q=4pi*b*R^4/4=pi*b*R^4

electric potential=KQ/R=K*pi*b*R^3

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