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

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SUMMARY

The discussion focuses on calculating the radius of a circular ring using the electric flux equation ϕ=EAcosΘ. A slope of m = 0.172 was derived from a plot of flux versus cosΘ, with an electric field strength E of 220. The user attempted to find the radius by manipulating the equation and using the area formula A = πr², but expressed uncertainty about the correctness of their approach. The gradient m is confirmed to represent the product EA, reinforcing the need for accurate calculations to derive the radius.

PREREQUISITES
  • Understanding of electric flux and its equation ϕ=EAcosΘ
  • Knowledge of trigonometric functions, specifically cosine and tangent
  • Familiarity with area calculations for circular shapes, specifically A = πr²
  • Basic algebraic manipulation skills for solving equations
NEXT STEPS
  • Review the derivation of electric flux and its applications in electromagnetism
  • Learn about the relationship between slope and electric field strength in graphical representations
  • Explore advanced trigonometric identities and their applications in physics problems
  • Study methods for accurately calculating the radius of circular shapes from given parameters
USEFUL FOR

Students studying electromagnetism, physics educators, and anyone involved in solving problems related to electric fields and circular geometries.

raz23
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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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Wouldn't the gradient of the line, m, just represent EA? And you know E already!
 

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