Electric Field of a Uniformly Charged Ring

In summary, to find the magnitude of the electric field on the axis of a uniformly charged ring with a radius of 8.1 cm and a total charge of 118 micro Coulombs, the Coulomb constant 8.98755e9 N M^2/C^2 must be used in the equation E= kq/r^2. The ring's axis is vertical and the integral should be taken over the charged area using cylindrical coordinates. The Ez component of the field produced by a point charge placed on the ring should be derived and multiplied by the factor determined by the linear charge density of the ring.
  • #1
ILoveCollege
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Homework Statement


A uniformly charged ring of radius 8.1 cm has a total charge of 118 micro Coulombs. The value of the Coulomb constant is 8.98755e9 N M^2/C^2. Find the magnitude of the electric field on the axis of the ring at 1.15 cm from the center of the ring. Answer in units of N/C.

Homework Equations


F= k Qq/ r^2
E= kq/r^2


The Attempt at a Solution


I tried subtracting 1.15 cm from 8.1 cm for "r" and plugged that "r" value in the F equation but that answer is wrong. By axis , do they mean horizontally (as in along the diameter) or vertically?
 
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  • #2
The ring axis is vertical (normal to the diameter).

You should sum the fields produced by each part of the ring (it's an integral over the ring).
 
  • #3
Why would I need to integrate? It already gives me the total charge for the ring. from what points would I integrate? 0 to 8.1?
 
  • #4
You need to integrate only over the charged area. In cylindrical coordinates it is

[tex]
\begin{array}{l}
r = 8.1 \text{cm}; \\
0 < \phi < 2\pi; \\
z = 0.
\end{array}
[/tex]

Since the ring is charged uniformly there is no need to calculte the integral explicitly.
Just derive the Ez component of the field produced by a point charge placed on the ring. Than multiple it by the factor determined by the linear charge density of the ring.
 

1. What is the formula for calculating the electric field of a uniformly charged ring?

The formula for calculating the electric field of a uniformly charged ring is E = kQz/(z^2+R^2)^(3/2), where E is the electric field, k is the Coulomb's constant, Q is the charge of the ring, z is the distance from the center of the ring, and R is the radius of the ring.

2. How does the electric field vary with distance from the center of the ring?

The electric field varies inversely with the distance from the center of the ring. This means that as the distance from the center increases, the electric field decreases. This relationship is described by the formula E = kQ/z^2, where k is the Coulomb's constant, Q is the charge of the ring, and z is the distance from the center of the ring.

3. What is the direction of the electric field at different points around the ring?

The direction of the electric field at different points around the ring is tangential to the circle at that point. This means that the electric field is perpendicular to a line drawn from the center of the ring to that point. This direction is described by the right-hand rule, where the thumb points in the direction of the electric field and the fingers curl in the direction of the current flow.

4. How does the charge of the ring affect the strength of the electric field?

The charge of the ring directly affects the strength of the electric field. As the charge of the ring increases, the electric field also increases. This relationship is described by the formula E = kQ/z^2, where k is the Coulomb's constant, Q is the charge of the ring, and z is the distance from the center of the ring. The electric field is directly proportional to the charge of the ring.

5. Is the electric field of a uniformly charged ring uniform?

No, the electric field of a uniformly charged ring is not uniform. It varies with distance from the center of the ring and is strongest at the center. As you move away from the center, the electric field decreases. Additionally, the direction of the electric field also varies at different points around the ring. However, the electric field is uniform in magnitude and direction along a circular path around the ring, as long as the distance from the center remains constant.

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