Concept explainers
A solid, insulating sphere of radius a has a uniform charge density throughout its volume and a total charge Q. Concentric with this sphere is an uncharged,
Figure P24.45 Problems 43 and 47.
(a)
Answer to Problem 24.54AP
Explanation of Solution
Given info: The radius of the inner insulating sphere is
Write the expression to calculate the charge density of the insulating sphere.
Write the expression to calculate the charge on the outer sphere at radius
Substitute
Conclusion:
Therefore, the charge contained within the sphere of radius
(b)
Answer to Problem 24.54AP
Explanation of Solution
Given info: The radius of the inner insulating sphere is
Write the expression to calculate the electric field.
Here,
Substitute
The expression of Coulomb’s law constant is,
Substitute
Conclusion:
Therefore, the magnitude of the electric field is
(c)
Answer to Problem 24.54AP
Explanation of Solution
Given info: The radius of the inner insulating sphere is
The sphere of radius
Conclusion:
Therefore, the charge contained within a sphere of radius
(d)
Answer to Problem 24.54AP
Explanation of Solution
Given info: The radius of the inner insulating sphere is
Write the expression to calculate the electric filed due to sphere.
The expression of Coulomb’s law constant is,
Substitute
Thus, the magnitude of the electric field is
Conclusion:
Therefore, the magnitude of the electric field is
(e)
Answer to Problem 24.54AP
Explanation of Solution
Given info: The radius of the inner insulating sphere is
The charge is exist only on the surface of the conductor due to which the electric field inside a conductor is zero.
Conclusion:
Therefore, the electric field for
(f)
Answer to Problem 24.54AP
Explanation of Solution
Given info: The radius of the inner insulating sphere is
The charge on the inner sphere is
Conclusion:
Therefore, the charge on the inner surface of the sphere for
(g)
Answer to Problem 24.54AP
Explanation of Solution
Given info: The radius of the inner insulating sphere is
The total charge on the outer sphere is zero. That means the charge on the outer surface of the outer sphere is
Conclusion:
Therefore, the charge on the outer surface of the sphere for
(h)
Answer to Problem 24.54AP
Explanation of Solution
Given info: The radius of the inner insulating sphere is
The surface charge density is inversely proportional to the surface area of the body.
Therefore, the sphere which has smallest surface area will have largest surface charge density.
Conclusion:
Therefore, the sphere which has the largest magnitude of surface charge density is inner surface of radius
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Chapter 24 Solutions
Physics for Scientists and Engineers
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