Linear Mass Density of current and wires

[splac6996]

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Homework Statement

The figure is a cross section through three long wires with linear mass density 43.0. They each carry equal currents in the directions shown. The lower two wires are 4.0 cm apart and are attached to a table.

Homework Equations

What current will allow the upper wire to "float" so as to form an equilateral triangle with the lower wires?

The Attempt at a Solution

I am not sure where to start could someone give me a hint at what to do?

 

[salmon]

Hint: A Repulsive force exists between straight current-carrying conductors carrying currents in opposite directions. By Ampere's law, each conductor generates a magnetic field around it and the forces acting on them are basically the forces of interaction between the magnetic fields. Any standard textbook should explain this phenomenon. Look up the Bio-Savart Law or try this link:

hyper-text-transfer-protocol://world-wide-web.physics.upenn.edu/~uglabs/lab_manual/force_between_conductors.pdf

(I'm not allowed to post URLs yet, so just copy-paste the above link in the address bar and rewrite the beginning of the link)

I'm thinking that the only reason why the upper conductor won't float is because of gravity. This means that you probably have to assume that the lower conductors are fixed, otherwise they'd fall too.

 

[Moetasim]

I would first start by identifying the variables and equations that are relevant to this problem. The linear mass density of a wire is given by the mass per unit length, which can be calculated using the equation:

linear mass density = mass/length

In this case, the linear mass density is given as 43.0, but the units are not specified. Therefore, we cannot directly calculate the mass or length of the wires. We also know that the lower two wires are 4.0 cm apart, but we do not know their lengths.

Next, we can use the equation for the force between two parallel current-carrying wires to determine the force between the upper and lower wires. This equation is given by:

F = (μ₀I₁I₂)/(2πd)

Where μ₀ is the permeability of free space, I₁ and I₂ are the currents in the two wires, and d is the distance between the wires.

Since we want the upper wire to "float", the forces acting on it must be balanced. This means that the force between the upper and lower wires must be equal to the weight of the upper wire. We can use this information to set up an equation and solve for the current in the upper wire that will allow it to float.

Finally, we can use the fact that the wires are arranged in an equilateral triangle to determine the relationship between the currents in the three wires. This will give us a system of equations that we can solve to find the current in the upper wire.

In summary, to solve this problem as a scientist, we need to first identify the relevant variables and equations, then set up and solve a system of equations to find the current in the upper wire that will allow it to float and form an equilateral triangle with the lower wires.