Concept explainers
Example 23.3 derives the exact expression for the electric field at a point on the axis of a uniformly charged disk. Consider a disk of radius R = 3.00 cm having a uniformly distributed charge of +5.20 μC. (a) Using the result of Example 23.3, compute the electric field at a point on the axis and 3.00 mm from the center. (b) What If? Explain how the answer to part (a) compares with the field computed from the near-field approximation E = σ/2ϵ0. (We derived this expression in Example 23.3.) (c) Using the result of Example 23.3, compute the electric field at a point on the axis and 30.0 cm from the center of the disk. (d) What If? Explain how the answer to part (c) compares with the electric field obtained by treating the disk as a +5.20-μC charged particle at a distance of 30.0 cm.
(a)
The electric field at a point on the axis at a distance
Answer to Problem 23.41P
The electric field at a point on the axis and
Explanation of Solution
The value of the charge is
The formula to calculate the surface charge density is,
The formula to calculate the area is,
Substitute
Substitute
The formula to calculate the electric field at a point from the center of a uniformly charged disk is,
Here,
Conclusion:
Substitute
Therefore, the electric field at a point on the axis and
(b)
The change in electric field when calculated using near field approximation.
Answer to Problem 23.41P
The magnitude of electric field when computed from near field approximation is
Explanation of Solution
The formula to calculate the electric field at a point from the center of a uniformly charged disk is,
Here,
Conclusion:
Substitute
The value of electric field for uniformly charged disk for a point
The formula to calculate the percentage change with respect to the field computed from near field approximation is,
Therefore, the magnitude of electric field when computed from near field approximation is
(c)
The electric field at a point on the axis at a distance
Answer to Problem 23.41P
The electric field at a point on the axis and
Explanation of Solution
The value of the charge is
The formula to calculate the surface charge density is,
The formula to calculate the area is,
Substitute
Substitute
The formula to calculate the electric field at a point from the center of a uniformly charged disk is,
Here,
Conclusion:
Substitute
Therefore, the electric field at a point on the axis and
(d)
The change in electric field at
Answer to Problem 23.41P
The magnitude of electric field obtained by treating the disk as a
Explanation of Solution
The formula to calculate the electric field of a charged particle is,
Here,
Substitute
the percentage change when part (c) is compared with the field obtained by treating the disk as a
The value of electric field for uniformly charged disk at a point
The value of the electric field while approximating the disc to be a point charge is
Conclusion:
The formula to calculate the percentage change when part (c) is compared with the field obtained by treating the disk as a
Therefore, the magnitude of electric field obtained by treating the disk as a point charge at a distance of
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Chapter 23 Solutions
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