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Concept explainers
(a)
To show that the electric field normal to the wire of length extending from
(a)
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Answer to Problem 22E
The electric field normal to the wire of length extending from
Explanation of Solution
Observe the Figure 16.18.
Write the expression for the linear charge density of the wire.
Here,
For an elemental length
From Figure 16.18a, the distance to an arbitrary point
This gives the magnitude of electric field due to the charge
Use equation (II) in (III).
The total field can be resolved into horizontal and vertical components given by,
Among them the horizontal components the electric field due to two elementary lengths of the wire equidistant from the center cancel each other. Thus,
From Figure 16.18b,
The vertical component of the elementary field is thus obtained as,
Thus the net electric field is obtained by integrating over the length of the wire. In this case the wire extends from
Use the standard integration formula Equation B.46 in Appendix B of the text book.
Use equation (VII) for determining the integral in equation (VI).
This shows that the electric field normal to the wire of length extending from
Conclusion:
Therefore, the electric field normal to the wire of length extending from
(b)
To show that the equation
(b)
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Answer to Problem 22E
The equation
Explanation of Solution
For infinitely long wire the integration limits in equation (VI) becomes
Conclusion:
Therefore, the equation
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Chapter 16 Solutions
General Physics, 2nd Edition
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