What is the Formula for Finding the Area of a Circular Coil?

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Homework Help Overview

The discussion revolves around understanding the formula for calculating the area of a circular coil, with specific focus on the presence of a factor of (1/4) in the area calculation. Participants are exploring the geometric implications of the coil's shape and dimensions.

Discussion Character

  • Conceptual clarification, Assumption checking

Approaches and Questions Raised

  • The original poster attempts to reconcile their understanding of the area of a coil with the formula they encountered, questioning the origin of the (1/4) factor. Other participants clarify the formula for the area of a circle and discuss the implications of using diameter versus radius.

Discussion Status

Participants are actively engaging in clarifying the definitions and dimensions involved in the problem. Some have provided insights into the relationship between diameter and radius, while others are still seeking a clearer explanation of the (1/4) factor.

Contextual Notes

There is mention of confusion regarding the dimensions used in the area calculation, with one participant acknowledging a mistake in considering volume instead of area. The original poster expresses uncertainty about the implications of a missing inner core in their understanding of the coil's area.

ikentrovik
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Homework Statement



Please see attached image file

I understand everything in this problem except I don't know how they got (1/4) in the area of a coil.

Can someone explain this? I have googled it and I am not getting a clear answer.

I thought the area of a coil could be (pi(r)^2)L where l is the length. But wouldn't this be a cyclinder? How would I find it when the inner core of the cyclinder is missing?

Thank you
 

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The coil is circular. The area of a circle is ##\pi r^2## and r is half of the diameter. The expression you gave is not an area, it has dimensions length^3.
 
You are right. I guess I gace volume. What I really don't understand is why there is a (1/4). Could you please explain why? Thank you.
 
Orodruin said:
The area of a circle is ##\pi r^2## and r is half of the diameter.

r = d/2 implies r^2 = d^2/4 ...
 
Oh ok thank you! What I did was divide the diameter in half right away. Thats why I was confused.
 

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