How can I find the number of turns in a solenoid winding?

[kdawg4]

A 30mH solenoid inductor is wound on a form 0.4 m in length and 0.1 m in diameter. A coil is tightly wound around the solenoid at its center. the coil resistance is 5.0 ohms. The mutual inductance of the coil and solenoid is 60μH. At a given instant, the current in the solenoid is 0.3A and is decreasing at a rate of 2.5A/s.


a) Find the number of turns in the winding of the solenoid
b) Find the induced emf at the given instant.
c) At the given instant, the flux linkage N(phi) for the solenoid is...


Hey guys, really need a nice simple answer here, thank you...I'm new to the forum by the way :D
At first I used the formula mu(n1)(n2)A/L equals the mutual inductance but now I am stumped since you have 2 unknowns and I don't know how to find one of them

 

[gneill]

A 30mH solenoid inductor is wound on a form 0.4 m in length and 0.1 m in diameter. A coil is tightly wound around the solenoid at its center. the coil resistance is 5.0 ohms. The mutual inductance of the coil and solenoid is 60μH. At a given instant, the current in the solenoid is 0.3A and is decreasing at a rate of 2.5A/s.

a) Find the number of turns in the winding of the solenoid
b) Find the induced emf at the given instant.
c) At the given instant, the flux linkage N(phi) for the solenoid is...


Hey guys, really need a nice simple answer here, thank you...I'm new to the forum by the way :D
At first I used the formula mu(n1)(n2)A/L equals the mutual inductance but now I am stumped since you have 2 unknowns and I don't know how to find one of them

Hi kdawg4, Welcome to Physics Forums.

Which part of the problem are you working on? Do you know the formula for the inductance of a solenoid?

 

[kdawg4]

I am currently workingon all three, and yes I know the formula for the inductance of a solenoid

 

[gneill]

I am currently workingon all three, and yes I know the formula for the inductance of a solenoid

Okay then, for part (a), what values in the formula for the inductance of the solenoid are unknowns (values that you haven't been given)?

 

[asteriatic]

Hi there! I am happy to help you with your questions. Let's break down the problem step by step.

a) To find the number of turns in the winding of the solenoid, we can use the formula for mutual inductance: M = μ0n1n2A/L. We know that μ0 is the permeability of free space (4π x 10^-7 H/m), A is the cross-sectional area of the solenoid (πr^2 where r is the radius of the solenoid), and L is the length of the solenoid. We are given the values for all of these parameters, except for n1 and n2. However, we can rearrange the formula to solve for n1 or n2. Let's solve for n1:

n1 = M/(μ0n2A/L)

Now, we can plug in the values we know and solve for n1:

n1 = (60 x 10^-6 H)/[(4π x 10^-7 H/m)(n2)(π(0.05 m)^2/0.4 m)]

n1 = 6.82 x 10^4 n2

b) To find the induced emf at the given instant, we can use the formula for emf in an inductor: emf = -L(dI/dt). We know the value for L (30 x 10^-3 H) and we are given the rate of change of current (2.5 A/s). We can plug these values in and solve for the induced emf:

emf = -(30 x 10^-3 H)(2.5 A/s) = -75 mV

c) At the given instant, the flux linkage N(phi) for the solenoid is equal to the mutual inductance (M) multiplied by the current in the solenoid (I). So, we can use the formula N(phi) = MI to find the flux linkage:

N(phi) = (60 x 10^-6 H)(0.3 A) = 18 μWb

I hope this helps! Let me know if you have any further questions. Welcome to the forum!