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and r is the radius from the center of the sphere. If the, the total charge of the sphere is Q and its maximum radius is R. What is the v

and r is the radius from the center of the sphere. If the, the total charge of the sphere is Q and its maximum radius is R. What is the v

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A non-uniformly charged insulating sphere has a volume charge density  that is expressed as 

p (rho) = beta(b) r

where beta  is a constant, and r is the radius from the center of the sphere. If the, the total charge of the sphere is Q and its maximum radius is R. What is the value for beta ?

 

Use the solution attached to solve for the problem.

 

Sol. By definition, the volume charge density is expressed infinitesimally as p= where in is the infinitesimal charge and E is the infinitesimal volume. V so, we have p = dq/ %3D so we can write this as dq = B dv But, dv = dr By substitution, we get the following dq = 4BT dr Using Integration operation and evaluating its limits, the equation, leads to Q = Rearranging, we get B =
Transcribed Image Text:Sol. By definition, the volume charge density is expressed infinitesimally as p= where in is the infinitesimal charge and E is the infinitesimal volume. V so, we have p = dq/ %3D so we can write this as dq = B dv But, dv = dr By substitution, we get the following dq = 4BT dr Using Integration operation and evaluating its limits, the equation, leads to Q = Rearranging, we get B =
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