How Is the Inductance of a Solenoid Calculated?

[Mike89]

Homework Statement

A constant current of 1A through a solenoid creates a magnetic flux of Φ=20mWb measured on the solenoid axis in the middle of the solenoid. What is the value of the solenoid inductance?

Homework Equations

here's what I've managed to find on the subject:

Φ=μ₀μ_rN²iA/l

L=μ₀μ_rN²A/l

where μ₀ = permitivity of free space, μ_r= permitivity of the core N is the number of turns, A is the cross sectional area, i is the current and l is the length of the solenoid

The Attempt at a Solution

Since we aren't given any other details like length or area all I can see to do is divide the magnetic flux by the current in order to get the Inductance. It seems suspiciously simple if this is the case since the guy that set it never sets anything straightforward.

So as far as I can tell the answer is L=20mWb/A

Thanks for any help or pointers

 

[Jhero]

.

Thank you for your question. You are correct in your attempt at a solution. The inductance of the solenoid can be calculated by dividing the magnetic flux by the current. However, there are a few things to keep in mind.

Firstly, the units for magnetic flux are actually Wb (webers), not mWb (milliwebers). So the correct unit for inductance would be H (henries) rather than mH (millihenries). This is important to note because the value of inductance will be different depending on which unit is used.

Secondly, the equation you have provided is for the inductance of an ideal solenoid, which assumes that the solenoid has a perfect cylindrical shape with no resistance or leakage. In reality, solenoids are not perfect and have some resistance and leakage, which can affect the inductance value.

Lastly, it is always a good idea to double check your calculations and make sure the units are consistent. In this case, if you use the correct units and plug in the given values, you should get an inductance value of 20 H, which seems reasonable for a solenoid with a flux of 20 Wb and a current of 1 A.

I hope this helps. Good luck with your studies.
Scientist