A solid sphere of radius R has a nonuniform charge distribution p=Ar², where A is a...
A solid sphere of radius R has a nonuniform charge distribution p=Ar², where A is a constant. Determine the total charge, Q, within the volume of the sphere.
Please explain and show work
Thank you
Homework Answers
volume element is dV = (4pi*r^2)*dr
then charge in volume element is dQ = rho*dV = rho*4*pi*r^2*dr
given that rho = A*r^2
then
dQ = 4pi*r^4*A*dr
total charge is Q = integral (dQ) = integral (A*4*pi*r^4*dr) =
A*4*pi*integral(r^4*dr) = A*4*pi*(r^5/5) = (4/5)*A*pi*r^5 is the
final answer
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