Concept explainers
(a)
To find the electric field strength at a distance
(a)
Explanation of Solution
Given:
Radius of a disk is
Surface charge density of the disk is
Distance of a point on axis is
Formula used:
Write the expression of the electric field magnitude on the axis of a uniformly charged disk.
Here,
Simplify above equation.
Write the expression of the electric field magnitude when
Here,
Write the expression of the electric field magnitude when
Write the expression for surface charge density.
Here,
Substitute
Here,
Substitute
Calculation:
Approximate value of electric field is calculated below.
Substitute
The exact value of the electric field is calculated below.
Substitute
Conclusion:
Thus, near the disk the approximate result and the exact result are near about same. There isa parity between two values.
(b)
To find the electric field strength at a distance
(b)
Explanation of Solution
Given:
Radius of a disk is
Surface charge density of the disk is
Distance of a point on axis is
Formula used:
Write the expression of the electric field magnitude on the axis of a uniformly charged disk.
Simplify above equation.
Here,
Write the expression of the electric field magnitude when
Here,
Write the expression of the electric field magnitude when
Write the expression for surface charge density.
Here,
Substitute
Here,
Substitute
Calculation:
Approximate value of electric field is calculated below.
Substitute
The exact value of the electric field is calculated below.
Substitute
Conclusion:
Thus, for the in case of electric field at a distance
(c)
To find the electric field strength at a distance
(c)
Explanation of Solution
Given:
Radius of a disk is
Surface charge density of the disk is
Distance of a point on axis is
Formula used:
Write the expression of the electric field magnitude on the axis of a uniformly charged disk.
Simplify above equation.
Here,
Write the expression of the electric field magnitude when
Here,
Write the expression of the electric field magnitude when
Write the expression for surface charge density.
Here,
Substitute
Here,
Substitute
Calculation:
Approximate value of electric field is calculated below.
Substitute
The exact value of the electric field is calculated below.
Substitute
Conclusion:
Thus, for large distances approximate result has a good agreement with the exact result. Two values are equal.
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Chapter 22 Solutions
Physics for Scientists and Engineers
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