Inductor wires are used in electrical circuits to store energy which builds up during the passage of electrical current. Inductors can also be referred to as reactors and their main property, their ability to store magnetic energy, is measured by their levels of "inductance" using standard units called "henries." Each inductor is made up of a wire coil with a series of loops that generate large magnetic fields and create stored energy during the flow of current. The length of the inductor wire has a direct impact on how much energy can be stored. Inductors are used in power supplies and various analogue radio transmitter circuits.

- Skill level:
- Challenging

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## Instructions

- 1
Write out the equation for calculating the inductance of a cylindrical coil, which is inductance (symbol L) is equal to the permeability of free space coefficient (mu zero) multiplied by the Nagaoka coefficient (K) multiplied by the number of turns present squared multiplied by the cross-sectional area of the coil in meters squared (A) divided by the length of the wire, also in meters.

- 2
Rearrange the equation so that the length of the wire coil is on the left of the equals sign, which gives length (l) equal to the permeability of free space coefficient (mu zero) multiplied by the Nagaoka coefficient (K) multiplied by the number of turns present squared multiplied by the cross-sectional area of the coil in meters squared (A) divided by the inductance (L). Write out the rearranged equation.

- 3
Find out the inductance (L) of the wire in henries (H). Examine the wire-based inductor to find the inductance because the value of inductance may be printed on the coil itself or read through the manufacturer's documentation that came with the component. Count the number of turns present in the coil (N) manually. Record the value.

- 4
Measure the diameter of the end coil using a straight rule. Record the value. Divide the diameter by 2 to get the radius of the coil. Record the value. Calculate the cross-sectional area of the coil in square meters (A) using the standard equation, which is cross-sectional area (A) equals pi (constant at 3.14) multiplied by the radius of the coil squared. Record the result.

- 5
Write the rearranged equation again, replacing the symbols with your own values. Insert values for the coefficients K and mu zero, which are 1 and 4 multiplied by pi to the power of 10, to the minus 7 henries per meter (H/m), respectively. Process the values using a calculator to reach a resultant value for the length of the wire. Record it at the bottom of the calculations, with the correct unit of length which is meters (m) in this case.

#### Tips and warnings

- The Nagoaka coefficient can be zero, 1 or more than 1, but if you wish to find out the length of wire required to maintain an inductance through an infinite single-layer coil, it is best to use a value of 1 for the fixed coefficient.
- Do not mix up units, such as meters with centimetres. Using different units in the same equation will result in an incorrect answer.