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 = dq/ = B 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 = 4)
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 = dq/ = B 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 = 4)
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![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 = dq/
= B
so we can write this as
dq = B
dV
But,
dV =
dr
By substitution, we get the following
dq = 4B
dr
Using Integration operation and evaluating its limits, the equation, leads to
Q =
Rearranging, we get
B =
4)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F86162901-a6b8-4437-9b2d-6941a880380f%2F763cfaad-6d98-486b-b579-4b319e7f88d0%2Feh8d5zt_processed.jpeg&w=3840&q=75)
Transcribed Image Text: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 = dq/
= B
so we can write this as
dq = B
dV
But,
dV =
dr
By substitution, we get the following
dq = 4B
dr
Using Integration operation and evaluating its limits, the equation, leads to
Q =
Rearranging, we get
B =
4)
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