Concept explainers
In a certain region of space, the electric field is
(a)
The volume density of electric charge at
Answer to Problem 24.42P
The volume density of electric charge at
Explanation of Solution
Given info: The electric field vector in the region of space is
Consider a Gaussian box of thickness
Formula to calculate the electric flux at
Here,
Write the expression for the electric field at
Substitute
Thus, electric field in the region of space at
The electric field enter into the box at
Substitute
Formula to calculate the electric flux at
Here,
Write the expression for the electric field at
The term
The electric field enter into the box at
Substitute
Write the expression for the net electric flux through the box.
Substitute
Write an alternate expression for the net electric flux from Gauss law.
Here,
Formula to calculate the volume of the Gaussian box is,
Here,
Formula to calculate the average charge enclosed inside the rectangular Gaussian surface is,
Here,
Replace
Substitute
Equate the equation (2) and (1) for same value of electric flux.
Substitute
Conclusion:
Therefore, the volume density of electric charge at
(b)
Whether the given region of space can be inside a conductor.
Answer to Problem 24.42P
No, the given region of space could not be inside a conductor.
Explanation of Solution
Given info: The electric field vector in the region of space is
According to the principle of Electromagnetism, in electrostatics free charges in a good conductor reside only on the surface. So the free charge inside the conductor is zero. So the field in it is caused by charges on the surface. Since charges are of the same nature and distribution is uniform, the electric fields cancel each other. No matter, what is the shape of the conductor as long as there is field inside it, electrons always rearrange themselves to make the net field zero.
But, the volume density of electric charge at
Conclusion:
Therefore, the given region of space could not be inside a conductor.
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Chapter 24 Solutions
Physics for Scientists and Engineers, Technology Update (No access codes included)
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