A non-uniformly charged insulating sphere has a volume charge density rho that is expressed as rho equals beta 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?
A non-uniformly charged insulating sphere has a volume charge density rho that is expressed as rho equals beta 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?
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A non-uniformly charged insulating sphere has a volume charge density rho that is expressed as rho equals beta 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?
Transcribed Image Text:QUESTION 1
A non-uniformly charged insulating sphere has a volume charge density p that is expressed as
p= Br
where B 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 B?
Sol.
By definition, the volume charge density is expressed infinitesimally as
p=
where in
is the infinitesimal charge and
is the infinitesimal volume.
So, we have
p = dql
= B
so we can write this as
dq = B
AP
But,
dV =
dr
By substitution, we get the following
dq = 4Bn
dr
Using Integration operation and evaluating its limits, the equation, leads to
Q =
Rearranging, we get
B =
4)
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