Average Magnetic Field Between 2 Conducting Rods

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• Gbl911
In summary, the speaker is building a small railgun using copper bars and neodymium magnets. They are also trying to mathematically describe the magnetic field created by the conducting rods, but are facing difficulties in deriving an expression for the average magnetic field across the gap. They have found a website that explains the process, but are still unsure about how it works. The speaker also mentions taking the finite radius of the wires into account and provides an equation for the average magnetic field. They are unsure about the purpose of finding this average field.

Gbl911

I am building small, simple version of a railgun using 2 copper bars and a couple of neodymium magnets to increase the magnetic field. I have also been trying to mathematically describe the magnetic field created by the conducting rods themselves. I am coming across some trouble when trying to derive an expression for the average magnetic field across the entire gap and would like some help.

You can write the magnetic field at anyone point in between the two bars as

(u*I)/(2*pi) * (1/r + 1/(d-r))
where u is mu, d is distance between the bars, I is the current, and r is the distance from the center of one bar to the point of interest.
I assume that I need to compute some form of integral but I'm not sure exactly what to integrate over and how to obtain the average field strength from that.
I found a website that details how they went about it but I still am not sure on why the way they did it works. Here is the link.
https://military-history.fandom.com/wiki/Railgun

You will notice that there is a problem as ## r \rightarrow 0 ##. So you need to take the finite radius of your wires into account.
If you do that the average is ## B_{avg} = ~(2\int_a^{d-a} \mu_0 I/2\pi r~ dr)/(d-2a) ## where ## a ## is the wire radius.
Not sure why you want this but there you go.

What is the concept of average magnetic field between 2 conducting rods?

The average magnetic field between 2 conducting rods refers to the measure of the magnetic field strength that is present in the space between two parallel conducting rods. This field is created by the electric current flowing through the conducting rods.

How is the average magnetic field between 2 conducting rods calculated?

The average magnetic field between 2 conducting rods can be calculated using the formula B = (μ0*I)/(2π*d), where B is the magnetic field strength, μ0 is the permeability of free space, I is the current flowing through the rods, and d is the distance between the rods.

What factors affect the average magnetic field between 2 conducting rods?

The average magnetic field between 2 conducting rods is affected by the magnitude of the current flowing through the rods, the distance between the rods, and the permeability of the medium surrounding the rods. Additionally, the presence of any external magnetic fields can also affect the average magnetic field.

What is the unit of measurement for average magnetic field between 2 conducting rods?

The unit of measurement for average magnetic field between 2 conducting rods is Tesla (T). However, in some cases, the unit of Gauss (G) is also used to measure magnetic field strength.

How is the average magnetic field between 2 conducting rods used in practical applications?

The average magnetic field between 2 conducting rods is used in various practical applications, such as electromagnets, electric motors, and generators. It is also used in the design and construction of electronic devices, such as speakers and headphones, to create magnetic fields that can interact with electrical signals.