Calculating Currents in Parallel Wires: Exploring B-Field Repulsion

In summary, two parallel wires with a distance of 2.50 cm apart will repel each other with a force per length of 1.00*10^-3 N/m. If one wire has a current of 100A, the current in the other wire can be found by using the equations for magnetic field and magnetic force. The force per length can be divided by the length to find the current in the other wire.
  • #1
tandoorichicken
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Two parallel wires repel each other with a force per length of 1.00*10^-3 N/m when spaced a distance of 2.50 cm apart. If one wire has a current of 100A, what is the current in the other wire?

Don't know where to start this one.
 
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  • #2
Two equations. First, the magnetic field that a wire with current creates at a distance of [tex]r[/tex] from it is:
[tex]B = \frac{\mu _0I}{2\pi r}[/tex]
Second, the magnetic force that operates on a wire with current inside a magnetic field is: (When the magnetic field is perpendicular to the direction of the current)
[tex]F_m = IBl[/tex]
To find the force per length, just divide it by [tex]l[/tex].

Now can you solve it? :smile:
 
  • #3


To calculate the current in the other wire, we can use the equation for the force between two parallel wires:

F = μ0*I1*I2*ℓ/2π*d

Where F is the force per length, μ0 is the permeability of free space (4π*10^-7 N/A^2), I1 and I2 are the currents in the two wires, ℓ is the length of the wires, and d is the distance between them.

In this case, we are given the force per length (F), the distance between the wires (d), and the current in one of the wires (I1). We can rearrange the equation to solve for I2:

I2 = 2π*d*F/(μ0*I1*ℓ)

Plugging in the given values, we get:

I2 = 2π*(0.025 m)*(1.00*10^-3 N/m)/(4π*10^-7 N/A^2*100A*1m)

Simplifying, we get:

I2 = 0.0005 A

Therefore, the current in the other wire must be 0.0005 A, or 500 mA. This shows that the current in the other wire is much smaller than the current in the first wire, which makes sense as the force per length is also much smaller. This demonstrates the principle of B-field repulsion, where two parallel wires with currents flowing in the same direction will repel each other.
 

1. What is a B-field wire?

A B-field wire, also known as a magnetic field wire, is a wire that produces a magnetic field when an electric current flows through it. It is typically made of a conductive material such as copper, and its strength and direction can be controlled by the amount and direction of the current flowing through it.

2. How is a B-field wire used?

B-field wires are commonly used in scientific experiments and industrial applications to manipulate and measure magnetic fields. They can also be used in devices such as electromagnets and magnetic sensors.

3. What is the difference between a B-field wire and a regular wire?

A regular wire is used to transmit electric current, while a B-field wire is used to create a magnetic field. Regular wires are made of a single conductor, while B-field wires may have multiple conductors wound together to increase the strength of the magnetic field.

4. How do B-field wires interact with other magnetic fields?

B-field wires can be attracted or repelled by other magnetic fields, depending on their direction and strength. They can also be used to shield or redirect magnetic fields in a certain direction.

5. Are B-field wires dangerous?

B-field wires are typically not dangerous on their own, but they can produce strong magnetic fields that may interfere with electronic devices or medical implants. It is important to handle and use B-field wires carefully and follow safety precautions to avoid any potential hazards.

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