Finding the inductance of a coil

In summary, the conversation discusses the calculation of magnetic flux and inductance for a circular coil with a radius of 0.10 m and 30 turns in the presence of an external magnetic field of 2.60 mT. While the correct answer for part a) is determined, there is confusion regarding part b) and the equation for inductance. The conversation concludes with a suggested equation for finding the inductance of the solenoid.
  • #1
fishingspree2
139
0

Homework Statement


A circular coil has a radius 0.10 m and 30 turns. An external magnetic field 2.60 mT is perpendicular to the coil. a) If there is no current, find the magnetic flux in the coil.
b) When current = 3.8 A in some direction, there is no more net flux in the coil. Find the inductance.

The Attempt at a Solution


I can do a) but I don't understand b. the correct answer of b) is 0.645 mH

a) flux = NB*PI*r^2 = 2.45 miliweber, this is the correct answer

b) L = N*flux / current. If I set flux=0 then I get inductance = 0, which makes no sense because inductance only depends of the geometry.

Please help =(
 
Last edited:
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  • #2
Suppose the external magnetic field didn't exist. What would be the magnetic field created by the solenoid? Net field is 0 when this is equal to 2.60 mT.
 
  • #3
I set B = -2.60 mT

which means that L = N*flux / current = n*-2.60 mT / current?

= (30*2.60*10^-3)/3.8 = 0.0205 H

not correct =(
 
  • #4
The magnetic field produced by the solenoid is B=μ0*N*I/L. When B=2.6 mT, net magnetic field is 0, so B=2.6 mT when I=3.8 A.

Now, what would be the equation for the flux through the solenoid, created by the solenoid itself? You can then find L using L = N*flux / current.
 
  • #5
Ok, B = μ0*n*i

the length of one turn is 2*Pi*R, the total length of the coil is N times that, so 2*Pi*R*N
n = number of turns / total length = N /[ (2*Pi*R*N) = 1 / (2*Pi*R)

so that B = μ0*i / 2*Pi*R

flux = B*Area = B*Pi*(R^2) = μ0*i*r / 2
so that L = N*flux / i = μ0*r*N / 2 = 1.88 * 10^-6 W, wrong answer

I have also tried multiplying the flux by N since there are N turns

please help =(
 
  • #6
Ideasrule told you that ...


B=2.6 mT when I=3.8 A ,,,,,, So find L the length of the solenoid by this equstion :

B=μ0*N*I/L

Where ,

B = 2.6e-3 T
N = 30 turns
I = 3.8 A
So L = ?

Then substitute the value of L in this equation to find the Inductance of the Solenoid :

L Solenoid's Inductance = μ0*N2*A / L Length Found

Thats it .


Just for more clarification here are the steps to get the last equation for solenoid's inductance :

B Solenoid = μ0*n*I

n = N/L , So B Solenoid = μ0*N*I/L

------------------------------------------------------------

[tex]\phi[/tex] B = N*B*A*Cos(00)

B Solenoid = μ0*N*I/L

So , [tex]\phi[/tex] B = N*(μ0*N*I/L )*A*Cos(00)

Cos(00) = 1

So , [tex]\phi[/tex] B = μ0*N2*I*A / L


-------------------------------------------------------------------------

The emf induced in N turns is N times the emf in one turn :

[tex]\epsilon[/tex] = - d[tex]\phi[/tex] B / dt

[tex]\epsilon[/tex] = - ( μ0*N2*A / L ) * (dI/dt)

--------------------------------------------------------------------------

Finally the inductance :

L Solenoid's Inductance = - [tex]\epsilon[/tex] / (dI/dt)

We will get finally :

L Solenoid's Inductance = μ0*N2*A / L Length Found

Good Luck ...
 
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Related to Finding the inductance of a coil

1. What is the formula for finding the inductance of a coil?

The formula for finding the inductance of a coil is L = (μ0 * N^2 * A)/l, where L is the inductance in henries, μ0 is the permeability of free space, N is the number of turns in the coil, A is the cross-sectional area of the coil, and l is the length of the coil.

2. How do I measure the inductance of a coil?

To measure the inductance of a coil, you will need a multimeter that has an inductance measurement function. Connect the leads of the multimeter to the two ends of the coil, and the multimeter will display the inductance value in henries.

3. Can the inductance of a coil change?

Yes, the inductance of a coil can change depending on factors such as the number of turns, the cross-sectional area, and the material of the coil. It can also change if the coil is placed in a magnetic field.

4. What is the unit of measurement for inductance?

The unit of measurement for inductance is henries (H). However, you may also see the unit millihenries (mH) or microhenries (μH) used for smaller values of inductance.

5. Why is it important to know the inductance of a coil?

The inductance of a coil is important because it determines the amount of energy stored in the magnetic field of the coil. It also affects the behavior of the coil in circuits, such as its ability to resist changes in current flow and its ability to induce voltage in nearby conductors.

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