Concept explainers
(a)
The expression for the electric field at point A located at a distance l above the mid-point of the rod.
(a)
Answer to Problem 79PQ
The expression for the electric field at point A located at a distance l above the mid-point of the rod is
Explanation of Solution
Sketch the diagram showing the five charges.
The x component of the electric field is zero based on the geometry.
Write the expression for the y component of the electric field.
Here,
Write the equation for the total electric field.
Conclusion:
Substitute
Substitute
Substitute
Substitute
Substitute
Substitute equations (III), (IV), (V), (VI) and (VII) in equation (II) to find
Thus, the expression for the electric field at point A located at a distance l above the mid-point of the rod is
(b)
The electric field at point A located at a distance l above the mid-point of the rod using the exact expression.
(b)
Answer to Problem 79PQ
The electric field at point A located at a distance l above the mid-point of the rod using the exact expression is
Explanation of Solution
Write the exact expression for the total electric field.
Here,
Conclusion:
Substitute
Thus, the electric field at point A located at a distance l above the mid-point of the rod using the exact expression is
(c)
Compare the approximate result with the exact result.
(c)
Answer to Problem 79PQ
The approximate result is
Explanation of Solution
Find the ratio of the approximate result with the exact result.
Conclusion:
Thus, the approximate result is
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Chapter 24 Solutions
Physics for Scientists and Engineers: Foundations and Connections
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