Suppose you wish to make a solenoid whose self-inductance is 1.2 mH. The inductor is to have a cross-sectional area of 1.2 10-3 m2 and a length of 0.048 m. How many turns of wire are needed?
Can you please clarify this for me. When I first post it my reponse was:
# turns= # of turns per meter length x l of solenoid.
I still don't get it please explain.
N=nl
http://hyperphysics.phy-astr.gsu.edu/hbase/electric/indsol.html#c1
You have length, area, inductance, you know mu. Solve for N, the number of turns of wire. The formula is straightforward.
Sure! Let's break down the formula N = nl to understand it.
In the formula N = nl, N represents the number of turns of wire in the solenoid, l represents the length of the solenoid, and n represents the number of turns per unit length (number of turns per meter).
To calculate the number of turns needed, we need to determine the value of n and multiply it by the length of the solenoid.
To find the value of n, we need to use the given information: The inductor has a cross-sectional area of 1.2 x 10^-3 m^2 (or 0.0012 m^2) and a self-inductance of 1.2 mH (or 0.0012 H).
The formula for self-inductance (L) of a solenoid is L = (μ₀n²A)/l, where μ₀ is the permeability of free space (4π x 10^-7 H/m), n is the number of turns per unit length, A is the cross-sectional area, and l is the length of the solenoid.
Now, rearranging the formula to solve for n:
n = √((Ll)/(μ₀A))
Substituting the given values:
n = √((0.0012 H x 0.048 m) / (4π x 10^-7 H/m x 0.0012 m^2))
Simplifying the equation:
n = √(0.0000576 / (4π x 10^-9))
n ≈ √(0.0000576 x 2.5 x 10^8)
Calculating the value of n:
n ≈ √(0.0000144 x 2.5 x 10^8)
n ≈ √(0.0036 x 10^8)
n ≈ √36
n ≈ 6
Now that we have the value of n (number of turns per unit length) as 6, we can calculate the total number of turns needed by multiplying it with the length of the solenoid.
Given the length of the solenoid as 0.048 m, we can plug it into the formula:
N = n x l
N = 6 turns/m x 0.048 m
N ≈ 0.288 turns
Therefore, you would need approximately 0.288 turns of wire for this solenoid. Since turns cannot be fractional, you would need to round up to the nearest whole number, so the final answer would be 1 turn.
Note: In this particular case, the rounding up is due to the fact that the calculated value of N is less than 0.5 turns.