Concept explainers
(a)
Total charge on the sphere
(a)
Explanation of Solution
Given:
Radius of non-
Formula used:
Write the expression for the total charge on the sphere.
Write the expression for the volume
Here,
Calculation:
Substitute
Substitute
Conclusion:
Thus, the total charge on the shell is
(b)
The electric field at a distance
(b)
Explanation of Solution
Given:
Radius of non-conducting sphere is
Formula used:
Write the expression for Gauss’s Law.
Here,
Substitute
Rearrange above expression for
Write the expression for charge enclosed by Gaussian surface for
Substitute
Simplify the above expression for
Calculation:
Since,
Substitute
Conclusion:
Thus, the electric field is
(c)
The electric field at a distance
(c)
Explanation of Solution
Given:
Radius of non-conducting sphere is
Formula used:
Write the expression for Gauss’s Law.
Here,
Substitute
Rearrange above expression for
Write the expression for charge enclosed by Gaussian surface for
Substitute
Simplify the above expression for
Calculation:
Since,
Substitute
Conclusion:
Thus, the electric field is
(d)
The electric field at a distance
(d)
Explanation of Solution
Given:
Radius of non-conducting sphere is
Formula used:
Write the expression for Gauss’s Law.
Here,
Substitute
Rearrange above expression for
Since the total charge on the sphere is enclosed by the Gaussian surface for
Since,
Calculation:
Substitute
Conclusion:
Thus, the electric field is
(e)
The electric field at a distance
(e)
Explanation of Solution
Given:
Radius of non-conducting sphere is
Formula used:
Write the expression for Gauss’s Law.
Here,
Substitute
Rearrange above expression for
Since the total charge on the sphere is enclosed by the Gaussian surface for
Since,
Calculation:
Substitute
Conclusion:
Thus, the electric field is
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Chapter 22 Solutions
Physics for Scientists and Engineers
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