Finding Inductance: Solving Homework Statement

[Josh225]

Homework Statement

See attached image.

Homework Equations

The only equation that I have learned to find inductance is : L= μ N² A / ι

However, when I do this, I get the incorrect answer. I am not so sure what is going on in the given solution and was wondering if somebody could explain that to me.The last step of the solution shows the equation that I stated, but how come you arent able to just plug numbers in directly?

Thank you in advanced!

The Attempt at a Solution

L= (4 Pi x 10^-7) (100²) (.25) / 1" = 3.14 x 10^-3[/B]

 

[Charles Link]

Homework Statement

See attached image.

Homework Equations

The only equation that I have learned to find inductance is : L= μ N² A / ι

However, when I do this, I get the incorrect answer. I am not so sure what is going on in the given solution and was wondering if somebody could explain that to me.The last step of the solution shows the equation that I stated, but how come you arent able to just plug numbers in directly?

Thank you in advanced!

The Attempt at a Solution

L= (4 Pi x 10^-7) (100²) (.25) / 1" = 3.14 x 10^-3[/B]

You need to work completely in MKS. You need the area A in square meters-I think you simply put in the diameter in inches. You also need the length L in meters. Your answer will then be in Henrys.

 

[Josh225]

Thanks!

 

[Josh225]

Also, when I plug all the correct numbers in and run the equation through, it comes out to .01568 and I have to move the decimal 3 places to the right (like the answer is in meters and I need to convert to millimeters).
I am honestly not so hot wih unit conversion, so I was wondering what an easy way would be for me to remember to move the decimal in this case.

Also, what is the significance of writing the answer in μH as opposed to just H?

 

[Charles Link]

$\mu$ means 1.0 E-6. I'd like to see your calculations, particularly for area $A$ to see what you got. The arithmetic here should be pretty routine. You might need a little practice with exponents, etc.

 

[Josh225]

$\mu$ means 1.0 E-6. I'd like to see your calculations, particularly for area $A$ to see what you got. The arithmetic here should be pretty routine. You might need a little practice with exponents, etc.

Hmmm I was under the impression that "μ" meant permeability and the letter following it represented a specific number (μo = 4 pi x 10^-7) (still can't find that pi button on here!).

I kinda "cheated" and looked up some of the conversion.. I really do need to practice them, but to find "A" I did:
Pi (d)² / 4
Pi (6.35 mm)² /4
= 31.7 m²

 

[Charles Link]

Hmmm I was under the impression that "μ" meant permeability and the letter following it represented a specific number (μo = 4 pi x 10^-7) (still can't find that pi button on here!).

I kinda "cheated" and looked up some of the conversion.. I really do need to practice them, but to find "A" I did:
Pi (d)² / 4
Pi (6.35 mm)² /4
= 31.7 m²

Those are millimeters you have there. 1mm=1.0E-3 m. This will give you a 1.0E-6 (m^2) when it gets squared. As area goes, this cylinder has a small area (cross section). Meanwhile 31.7 m^2 is about as big as an average living room.

 

[Josh225]

Those are millimeters you have there. 1mm=1.0E-3 m. This will give you a 1.0E-6 (m^2) when it gets squared. As area goes, this cylinder has a small area (cross section). Meanwhile 31.7 m^2 is about as big as an average living room.

Oh dang haha. Quite a difference. So it would be 31.7 μm²... Which would actually equal 3.17E-5 m, right?

 

[Charles Link]

Oh dang haha. Quite a difference. So it would be 31.7 μm²... Which would actually equal 3.17E-5 m, right?

You need to call it 3.17 E-5 "m^2", (square meters), but otherwise correct.

 

[Josh225]

You need to call it 3.17 E-5 "m^2", (square meters), but otherwise correct.

Strange.. In my book it's expressed as 31.7 μm².

 

[Charles Link]

Strange.. In my book it's expressed as 31.7 μm².

That part is ok . I was simply correcting the missing "2" on your m^2 (at the end of post #8).

 

[Josh225]

Oh! I see. Thank you for the info!

 

[NascentOxygen]

Hmmm I was under the impression that "μ" meant permeability and the letter following it represented a specific number (μo = 4 pi x 10-7)

It depends on context. Certainly, $\mu$ is the symbol for permeability, both as $\mu_{\scriptsize 0}$ and relative permeability, $\mu_r$. But you have also seen $\mu$ denoting the coefficient of friction of a surface; and the most common encounter is in association with units as a dimensionless multiplier meaning ×10^-6 and written as a prefix pronounced "micro", e.g., $7\ \mu V$.

 

[Charles Link]

It depends on context. Certainly, $\mu$ is the symbol for permeability, both as $\mu_{\scriptsize 0}$ and relative permeability, $\mu_r$. But you have also seen $\mu$ denoting the coefficient of friction of a surface; and the most common encounter is in association with units as a dimensionless multiplier meaning ×10^-6 and written as a prefix pronounced "micro", e.g., $7\ \mu V$.

Very good comment. For the OP: In the second part of the above problem, they use the letter $\mu_r$ for the permeability of the iron inside the inductor. To avoid any confusion, it would be nice if they could use a different letter for both the magnetic $\mu_o=4 \pi E-7$ and the magnetic $\mu_r =2000$, because the $\mu$ in $\mu m^2$ and $\mu H$ means 1.0E-6, but in the magnetic theory, $\mu$ (in this problem with a subscript) is the letter that the science people have chosen for these magnetic parameters.