Concept explainers
(a) Consider a uniformly charged, thin-walled, right circular cylindrical shell having total charge Q, radius R, and length ℓ. Determine the electric field at a point a distance d from the right side of the cylinder as shown in Figure P23.9. Suggestion: Use the result of Example 23.2 and treat the cylinder as a collection of ring charges. (b) What If? Consider now a solid cylinder with the same dimensions and carrying the same charge, uniformly distributed through its volume. Use the result of Example 23.3 to find the field it creates at the same point.
Figure P23.9
(a)
The electric field at a point a distance
Answer to Problem 9P
The electric field at a point a distance
Explanation of Solution
Given info: The total charge is
Consider one ring with thickness
Figure (1)
The formula used to find the electric field at the chosen point is,
Here
Integrate on both side from the limits
Conclusion:
Therefore, the electric field at a point a distance
(b)
The electric field created at the same point by a solid cylinder with same dimensions and carrying the same charge.
Answer to Problem 9P
The electric field created at the same point by a solid cylinder with same dimensions and carrying the same charge is
Explanation of Solution
Given info: The total charge is
The charge per unit area is,
Here,
The field produced by the one disk is,
Here,
Integrate on the both side to get the total electric field
Further solve the above expression.
Conclusion:
Therefore, the electric field created at the same point by a solid cylinder with same dimensions and carrying the same charge is
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