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Solved: A solid conducting sphere with radius R carries a
Chapter 22, Problem 50P(choose chapter or problem)
Problem 50P
A solid conducting sphere with radius R carries a positive total charge Q. The sphere is surrounded by an insulating shell with inner radius R and outer radius 2R. The insulating shell has a uniform charge density \(\rho\). (a) Find the value of so that the net charge of the entire system is zero. (b) If has the value found in part (a), find the electric field (magnitude and direction) in each of the regions \(0<r<R, R<r<2 R\), and \(r>2 R\). Show your results in a graph of the radial component of \(\vec{E}\) as a function of r. (c) As a general rule, the electric field is discontinuous only at locations where there is a thin sheet of charge. Explain how your results in part (b) agree with this rule.
Equation Transcription:
Text Transcription:
Rho
0<r<R,R<r<2R
r>2R
Vector E
Questions & Answers
QUESTION:
Problem 50P
A solid conducting sphere with radius R carries a positive total charge Q. The sphere is surrounded by an insulating shell with inner radius R and outer radius 2R. The insulating shell has a uniform charge density \(\rho\). (a) Find the value of so that the net charge of the entire system is zero. (b) If has the value found in part (a), find the electric field (magnitude and direction) in each of the regions \(0<r<R, R<r<2 R\), and \(r>2 R\). Show your results in a graph of the radial component of \(\vec{E}\) as a function of r. (c) As a general rule, the electric field is discontinuous only at locations where there is a thin sheet of charge. Explain how your results in part (b) agree with this rule.
Equation Transcription:
Text Transcription:
Rho
0<r<R,R<r<2R
r>2R
Vector E
ANSWER:
Solution 50P
We need to find the value of charge density when the net charge of the system is zero.
The volume of the insulating shell
Therefore, charge on the shell
Hence, the net charge
(a) When the net charge is 0.
Therefore, for the net charge to be zero, the value of has to be