Solved: A solid conducting sphere with radius R carries a

Chapter 22, Problem 50P

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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

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

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