Force between two parallel wires

In summary, in this problem, two parallel wires are discussed, one carrying a current of 48 A and the other in suspension 15 cm below. The task is to determine the magnitude and direction of the current in the lower wire and whether it is in stable equilibrium. The equation F/l= u.I1I2/2(3.14)d is used to calculate the magnetic force, with "u" representing the permeability of free space. Since the second wire is not falling down, the current in both wires must be in the same direction and the magnetic force from the wire above must be countering the second wire's weight. The length of the wire is not needed to calculate the force, as the equation gives the force
  • #1
urszula
5
0

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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  • #2
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...
 
  • #3


I would approach this problem by first considering the basic principles of electromagnetism. The force between two parallel wires is described by the equation 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.

Using this equation, we can calculate the force between the two wires. In this case, we know that one wire has a current of 48 A and the other is made of 2.5 mm diameter copper wire, but we do not know the current in the second wire. We can use the fact that the second wire is in magnetic suspension to determine the magnitude and direction of the current in the lower wire.

To achieve magnetic suspension, the force of gravity acting on the wire must be balanced by the magnetic force between the two wires. This means that the force of gravity, mg, will be equal to the force between the wires, μ0I1I2/2πd. We can rearrange this equation to solve for I2, giving us I2 = 2πmd/μ0I1.

Plugging in the given values, we get I2 = (2π)(0.0025 m)(9.8 m/s^2)/(4π x 10^-7 T.m/A)(48 A) = 0.081 A. This means that the current in the lower wire is 0.081 A in the same direction as the upper wire.

As for the stability of the lower wire, it is in a state of stable equilibrium. This means that if the lower wire were to be slightly disturbed, it would return to its original position due to the balancing forces of gravity and magnetism.

In summary, the magnitude and direction of the current in the lower wire is 0.081 A in the same direction as the upper wire. The lower wire is in stable equilibrium.
 

1. What is the force between two parallel wires?

The force between two parallel wires is the electrostatic force of attraction or repulsion between the two wires due to the presence of electric charges.

2. How is the force between two parallel wires calculated?

The force between two parallel wires is calculated using Coulomb's law, which states that the force between two charged particles is directly proportional to the product of their charges and inversely proportional to the square of the distance between them.

3. What factors affect the force between two parallel wires?

The force between two parallel wires is affected by the distance between the wires, the amount of charge on each wire, and the type of charge (positive or negative).

4. Can the force between two parallel wires be attractive?

Yes, the force between two parallel wires can be attractive or repulsive, depending on the charges on the wires. If the wires have opposite charges, the force will be attractive, while if they have the same charge, the force will be repulsive.

5. How does the force between two parallel wires change if the wires are moved closer together?

If the wires are moved closer together, the force between them will increase because the distance between the charges decreases. This follows Coulomb's law, which states that the force is inversely proportional to the square of the distance between the charges.

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