Force between two parallel wires

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A horizontal wire carries a current of 48 A, while a second parallel copper wire, suspended 15 cm below, must have a current in the same direction to remain stable. The magnetic force between the wires counteracts the weight of the lower wire, which is crucial for its equilibrium. The equation F/l = u.I1I2/2(πd) can be used to analyze the forces, focusing on a one-meter length for calculations. To determine the weight of the lower wire, its diameter and copper density can be used to find its mass. Understanding these relationships is essential for solving the problem effectively.
urszula
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Homework Statement



Along horizontal wire carries a current at 48 A. A second wire,made of 2.5 mm diameter copper wire and parallel to the first,is kept in suspension magnetically 15 cm below.Determine the magnitude and direction of the current in the lower wire.Is the lower wire in stable equilibrium?

Homework Equations


F/l= u.I1I2/2(3.14)d

u. -permeability of free space

The Attempt at a Solution



The second wire is not falling down so the current in both wires must be the same direction.I dont't have any idea how to get the force ,because there is no length and mass.
 
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urszula said:
The second wire is not falling down so the current in both wires must be the same direction.I dont't have any idea how to get the force ,because there is no length and mass.

Since the second wire is hovering steadily, the magnetic force from the wire above it must be countering the second wire's weight. You don't need to know the length because your equation gives the magnetic force per length. So just consider, say, the forces on one meter of wire.

What does one meter of this wire weigh? You are given a diameter for it and are told it is made of copper, so you can look up its density. This will allow you to find the mass and weight...
 
The book claims the answer is that all the magnitudes are the same because "the gravitational force on the penguin is the same". I'm having trouble understanding this. I thought the buoyant force was equal to the weight of the fluid displaced. Weight depends on mass which depends on density. Therefore, due to the differing densities the buoyant force will be different in each case? Is this incorrect?

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