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

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To find the radius of a circular ring from the given equation, the electric flux is calculated using the formula ϕ=EAcosΘ, where E is the electric field strength. The slope m of the flux versus cosTheta plot is identified as 0.172, which may represent the product EA. The attempt to derive the radius involves using the area formula A=πr² and manipulating the values derived from the slope and electric field. However, there is uncertainty regarding the correctness of the calculations, particularly in how the gradient relates to EA and the subsequent steps taken. Clarification on the relationship between the slope and the electric field is needed to ensure accurate radius determination.
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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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