Concept explainers
A uniformly charged ring of radius 10.0 cm has a total charge of 75.0 μC. Find the electric field on the axis of the ring at (a) 1.00 cm, (b) 5.00 cm, (c) 30.0 cm, and (d) 100 cm from the center of the ring.
(a)
The electric field on the axis of a ring at
Answer to Problem 3P
The electric field on the axis of a ring at
Explanation of Solution
Given info: The radius of the uniformly charged ring is
From the Coulomb’s law the formula to calculate the electric field at any distance on the axis due to a uniformly charged ring.
Here,
The proportionality constant
Here,
Substitute
The charge on the ring is positive so the direction of the electric field is away from the center of the ring.
Substitute
Conclusion:
Therefore, the electric field on the axis of a ring at
(b)
The electric field on the axis of a ring at
Answer to Problem 3P
The electric field on the axis of a ring at
Explanation of Solution
Given info: The radius of the uniformly charged ring is
The charge on the ring is positive so the direction of the electric field is away from the center of the ring.
Substitute
Conclusion:
Therefore, the electric field on the axis of a ring at
(c)
The electric field on the axis of a ring at
Answer to Problem 3P
The electric field on the axis of a ring at
Explanation of Solution
Given info: The radius of the uniformly charged ring is
The charge on the ring is positive so the direction of the electric field is away from the center of the ring.
Substitute
Conclusion:
Therefore, the electric field on the axis of a ring at
(d)
The electric field on the axis of a ring at
Answer to Problem 3P
The electric field on the axis of a ring at
Explanation of Solution
Given info: The radius of the uniformly charged ring is
The charge on the ring is positive so the direction of the electric field is away from the center of the ring.
Substitute
Conclusion:
Therefore, the electric field on the axis of a ring at
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