How to find a radius of a circular ring from a given equation

In summary, the conversation discussed a circular ring with an unknown figure, and the angle theta between the electric field direction and a unit vector normal to the surface area of the ring. A plot of flux versus costheta revealed a slope of m = 0.172. The equation used was ϕ=EAcosΘ. The individual attempted to solve for ϕ and theta using various calculations, but questioned the accuracy of their solution.
  • #1
raz23
2
0

Homework Statement


There wasn't a figure given. All that was given was that the figure is a circular ring. Theta is the angle between the electric field direction and a unit vector normal to the surface area of the ring. Flux versus costheta was plotted and a slope was found to be m = 0.172. E = 220.


Homework Equations


ϕ=EAcosΘ


The Attempt at a Solution


I took the tan-1 of 0.172 and then the cos of 9.76 and threw 9.76 for ϕ and .99 or the cos of 9.76 for theta and then divided 9.76 by .99. I thought the area was pi r2. I multiplied 220 by pi and then divided that answer by 9.86 or 9.76/.99. And then took the square root of that. Is this correct? I'm thinking it's not.
 
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  • #2
Wouldn't the gradient of the line, m, just represent EA? And you know E already!
 

Related to How to find a radius of a circular ring from a given equation

What is the equation for finding the radius of a circular ring?

The equation for finding the radius of a circular ring is:
r = (R1 + R2)/2
Where r is the radius of the ring, R1 is the outer radius, and R2 is the inner radius.

How do I determine the inner and outer radius of a circular ring?

The inner and outer radius of a circular ring can be determined by measuring the distance from the center of the ring to the inner and outer edges, respectively.

What if I am given the circumference or diameter of the ring instead of the equation?

If you are given the circumference (C) or diameter (D) of the ring, you can use the following equations to find the radius:
r = C/(2π)
r = D/2
Where π is approximately 3.14.

Can the equation for finding the radius of a circular ring be used for all types of rings?

Yes, the equation r = (R1 + R2)/2 can be used for all types of circular rings, including concentric, non-concentric, and overlapping rings.

Is there a specific unit of measurement that needs to be used for the equation?

The unit of measurement used for the equation will depend on the units used for the inner and outer radius. As long as the units are consistent, the resulting radius will be in the same unit of measurement.

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