Radius of Toroid given Surface to Volume Ratio and Total Surface Area Calculator

Formula Used:

\[ r = \frac{TSA}{2 \pi A_{Cross Section} \left( \frac{RA}{V} \right)} \]

Total Surface Area of Toroid (TSA):

m²

Cross Sectional Area of Toroid (A_Cross Section):

m²

Surface to Volume Ratio of Toroid (RA/V):

1/m

Radius of Toroid (r):

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1. What is the Radius of Toroid?

The Radius of Toroid is the line connecting the center of the overall Toroid to the center of a cross-section of the Toroid. It is a fundamental geometric parameter in toroidal structures.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ r = \frac{TSA}{2 \pi A_{Cross Section} \left( \frac{RA}{V} \right)} \]

Where:

\( r \) — Radius of Toroid (m)
\( TSA \) — Total Surface Area of Toroid (m²)
\( A_{Cross Section} \) — Cross Sectional Area of Toroid (m²)
\( \frac{RA}{V} \) — Surface to Volume Ratio of Toroid (1/m)
\( \pi \) — Archimedes' constant (approximately 3.14159)

Explanation: This formula calculates the radius of a toroid based on its total surface area, cross-sectional area, and surface to volume ratio.

3. Importance of Radius Calculation

Details: Calculating the radius of a toroid is essential in various engineering and physics applications, particularly in electromagnetism where toroidal coils are used in transformers and inductors.

4. Using the Calculator

Tips: Enter total surface area in m², cross-sectional area in m², and surface to volume ratio in 1/m. All values must be positive numbers.

5. Frequently Asked Questions (FAQ)

Q1: What is a toroid?
A: A toroid is a doughnut-shaped solid object generated by revolving a circle around an axis coplanar with the circle.

Q2: What are typical applications of toroids?
A: Toroids are commonly used in electromagnetics for transformers, inductors, and tokamak fusion reactors due to their efficient magnetic field containment.

Q3: How does the surface to volume ratio affect the radius?
A: A higher surface to volume ratio typically results in a smaller radius for a given surface area and cross-sectional area.

Q4: Can this formula be used for any toroid shape?
A: This formula applies to toroids with circular cross-sections. For other cross-sectional shapes, different formulas may be required.

Q5: What units should be used for input values?
A: All input values should use consistent SI units: meters for length, square meters for area, and 1/meters for surface to volume ratio.