Electromagnetism - Find length of coil

In summary, the problem asks to calculate the length of an iron-free cylindrical coil with 9400 turns, 0.6cm thickness, and an inductance of 68 mH. The formula used is L = N^2 * uo * ur * A / l, where uo is the magnetic field constant and ur is the relative permeability of the material. Since the core is iron-free, the expected material would have a high relative permeability for easier calculations. For a 0.6cm thick wire, the cross-sectional area would be calculated in meters squared.
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Homework Statement


Calculate the length l of an an iron-free cylindrical coil if it has 9400 turns (N), a thickness of 0.6cm and an inductance L = 68 mH. Take magnetic field constant [tex]\mu[/tex]o = 4[tex]\pi[/tex] x 10-7 Wb/Am

(a) l = 63mm
(b) l = 54mm
(c) l = 46mm
(d) l = 36mm

Homework Equations



L = N2 [tex]\mu[/tex]o [tex]\mu[/tex]r A / l

The Attempt at a Solution



0.068 = (9400)2 x ( 4[tex]\pi[/tex] x 10-7) [tex]\mu[/tex]r A / l

how to calculate if [tex]\mu[/tex]r and A are not given??
 
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  • #2
Given that the core is iron-free, what sort of material would you expect to find there? This material has a very nice relative permeability for calculations!

If you have a (circular cross section of a) piece of wire that is 0.6cm thick (diameter), what is the (cross sectional) Area of this wire?

*NB: Beware of units, as 'l' is in meters, 'A' is in meters squared and 'L' is in Henry's.
 
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What is electromagnetism and how does it relate to finding the length of a coil?

Electromagnetism is the study of the relationship between electricity and magnetism. In the context of finding the length of a coil, electromagnetism is important because it explains how magnetic fields are created when a current flows through a wire, and how the strength of the magnetic field is affected by the length of the wire.

What is a coil and how is it related to electromagnetism?

A coil is a length of wire wound into a series of loops or turns. When a current flows through a coil, it creates a magnetic field around the coil. This is due to the relationship between electricity and magnetism, known as electromagnetism. The strength and direction of the magnetic field can be controlled by changing the number of loops or turns in the coil.

How do you find the length of a coil?

The length of a coil can be found by using the formula L = μN²A/l, where L is the length of the coil, μ is the permeability of the material, N is the number of turns in the coil, A is the cross-sectional area of the coil, and l is the magnetic field strength. This formula takes into account the relationship between electromagnetism and the length of a coil, as well as other variables such as the material and cross-sectional area of the coil.

What are some practical applications of finding the length of a coil?

There are many practical applications of finding the length of a coil, including designing and building electromagnets for use in motors, generators, and other electrical devices. Knowing the length of a coil can also be useful in determining the strength of a magnetic field and how it will interact with other materials or objects in its vicinity.

Are there any limitations to using electromagnetism to find the length of a coil?

There are a few limitations to consider when using electromagnetism to find the length of a coil. One limitation is that the formula used to calculate the length of a coil assumes a uniform magnetic field, which may not always be the case in real-life situations. Additionally, the material of the coil and the presence of other nearby magnetic fields can also affect the accuracy of the calculation. It is important to carefully consider these factors when using electromagnetism to find the length of a coil.

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