Why Does Rearranging an Inductor Yield Different Magnetic Fields?

In summary, the first way to solve this problem is to find the magnetic field created by the original inductor when it is connected to the battery. The second way is to find the magnetic field created by the new inductor when it is connected to the battery. The first way is easier because the magnetic field is the same no matter which inductor is used.
  • #1
matej1408
4
0
I found two ways to solve this problem, but I get two different solutions, it's confusing because I can't see the flaw in wrong solution.
1. Homework Statement

Long cylindrical inductor of diameter D1 and inductance L1 is connected to battery and creates magnetic field B1. Inductor is then rearranged to new inductor of diameter D2 and inductance L2. Find magnetic field B2 which is created when "new" inductor is connected to the same battery as before. Assume that length of wire is much larger then length on inductor.

Homework Equations


L=μN2S/l
B=μNi/l
i-current, l-length of coil

The Attempt at a Solution


1st way(correct):[/B]
B1=μN1i/l1 => μN1/l1=B1/i
L1=μN12S1/l1
L1=N1S1B1/i
current is same in both case so:
L2=N2S2B2/i
dividing and rearranging_
L1=N1S1B1/i
L2=N2S2B2/i
B2=B1N1S1L2/(N2S2L1)
wire is same length in both case so:
h- thickness of wire
N1hD1π=N2hD2π
N1/N2=D2/D1
and S∝D2
B2=B1D1L2/(D2L1)
2nd way:
Bn=μNni/ln => B2= B1N2l1/(l2N1)
Ln=μNn2Sn/ln
Nn=√(Lnln /(μSn))
so N2/N1=√(L2l2S1/(L1l1S2))
substituting: B2= B1√(L2l1S1/(L1l2S2))
wire is same length so: Dπl= constant => l1/l2=D2/D1
and and S∝D2 =>
B2=B1√(D1L2/(D2L1))
 
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  • #2
Hello, and welcome to PF!

matej1408 said:
1st way(correct):
wire is same length in both case so:
h- thickness of wire
N1hD1π=N2hD2π
I'm not quite sure why you have a factor of h on each side of the above equation. In any case, it does lead to the following
N1/N2=D2/D1
which I believe is correct.

Keep in mind that either solenoid can have more than one layer of wraps of wire.

2nd way:
wire is same length so: Dπl= constant => l1/l2=D2/D1

How is Dπl related to the length of wire?
 
  • #3
When you connect battery to an inductor the current does not stabilize but ramps up at a constant rate di/dt = V/L. So how a re you comparing currents? the problem also implies that the inductor is changed 'on the fly' while current is flowing, which itself constitutes a V = i dL/dt problem in addition to the usual V = L di/dt one.
Bottom line, the problem is hard to understand, at least for me.
 
  • #4
I see where i was wrong, I assumed that there is just one layer but there isn't, thank you TSny.
Coil has some resistance and when is connected to DC there is no voltage change=> current is constant
 
  • #5


I would recommend double-checking your calculations and equations to ensure accuracy. It is possible that the incorrect solution may have a mistake in the calculation or use of equations. Additionally, it may be helpful to physically visualize the rearrangement of the inductor and how it may affect the magnetic field. Another approach could be to compare your solutions to known principles and laws, such as Faraday's Law or the equations for inductance and magnetic field. Ultimately, it is important to carefully analyze and troubleshoot any discrepancies in your solutions to determine the correct answer.
 

1. What is an inductor?

An inductor is an electronic component that stores energy in the form of a magnetic field. It is typically made up of a wire coil and is used in circuits to control the flow of electrical current.

2. Why would I need to rearrange an inductor?

Rearranging an inductor can be necessary in order to optimize the performance of a circuit. It may also be done in order to change the properties of the inductor, such as its inductance or resistance.

3. How do I rearrange an inductor?

The process of rearranging an inductor involves changing either the physical structure of the inductor or the components of the circuit that it is connected to. This can include adjusting the number of turns in the coil, changing the material of the core, or altering the placement of the inductor within the circuit.

4. What are some common methods for rearranging an inductor?

Some common methods for rearranging an inductor include adding or removing turns from the coil, changing the core material, using different wire gauges, and altering the circuit's layout. These changes can have an impact on the inductor's inductance, resistance, and other properties.

5. What are some potential applications for rearranging an inductor?

Rearranging an inductor can be useful in a variety of applications, such as in power supplies, filters, and oscillators. It can also be used to fine-tune the performance of electronic devices and circuits, and to optimize their efficiency and stability.

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