Solution Found!
Solved: A Sphere in a Sphere. A solid conducting sphere
Chapter 22, Problem 22.44(choose chapter or problem)
A solid conducting sphere carrying charge \(q\) has radius \(a\). It is inside a concentric hollow conducting sphere with inner radius \(b\) and outer radius \(c\). The hollow sphere has no net charge.
(a) Derive expressions for the electric field magnitude in terms of the distance \(r\) from the center for the regions \(r<a, a<r<b, b<r<c \text {, and } r>c\).
(b) Graph the magnitude of the electric field as a function of \(r\) from \(r=0\) to \(r=2c\)
(c) What is the charge on the inner surface of the hollow sphere?
(d) On the outer surface?
(e) Represent the charge of the small sphere by four plus signs. Sketch the field lines of the system within a spherical volume of radius \(2c\).
Questions & Answers
QUESTION:
A solid conducting sphere carrying charge \(q\) has radius \(a\). It is inside a concentric hollow conducting sphere with inner radius \(b\) and outer radius \(c\). The hollow sphere has no net charge.
(a) Derive expressions for the electric field magnitude in terms of the distance \(r\) from the center for the regions \(r<a, a<r<b, b<r<c \text {, and } r>c\).
(b) Graph the magnitude of the electric field as a function of \(r\) from \(r=0\) to \(r=2c\)
(c) What is the charge on the inner surface of the hollow sphere?
(d) On the outer surface?
(e) Represent the charge of the small sphere by four plus signs. Sketch the field lines of the system within a spherical volume of radius \(2c\).
ANSWER:Step 1 of 5
We need to use Gauss law to find the electric field of a system with a conducting sphere inside a hollow conducting sphere. We are also asked to graph the field as a function of the radius.
We have to find the charge on the inner and outer sphere and a sketch of field lines within spherical volume of radius \(r=2c\).
Gauss law states that,” the total electric flux through an enclosed surface is equal to a constant times the total charge enclosed by the surface.”
\(\oint E \cdot d A=\frac{Q_{e n c l}}{\epsilon_{o}}\)
