4a A charge, q, is distributed uniformly over a solid sphere of radius R. We nee

Question

4a A charge, q, is distributed uniformly over a solid sphere of radius R. We need to break the sphere up into infinitesimal pieces such that its density is constant over the extent of each piece. Write the expression, dq, that represents the infinitesimal charge on a spherical shell of radius r and infinitesimal thickness dr (Do you see that the density is constant over the extent of the shell?) 4b A charge, q, is distributed non-uniformly over a solid sphere of radius R. We need to break the sphere up into infinitesimal pieces such that its density is constant over the extent of each piece. The charge distribution is described by the expression pabr write the expression, dq, that represents the infinitesimal charge on a spherical shell of radius r and infinitesimal thickness dr

Explanation / Answer

4a. charge density = total charge / volume

= Q / (4 pi R^3 / 3)

= 3 Q /(4 pi R^3)

so dq = (charge denisty) (dV)

dq = (3 Q / (4 pi R^3)) (4 pi r^2 dr)

dq = (3 Q r^2 / R^3) dr

4b. dq = (rho) (4 pi r^2 dr)

dq = b r 4 pi r^2 dr

dq = (4 pi b r^3) dr

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