Magnetic Forces on Current-Carrying Wires: Attraction & Repulsion

In summary: So, in summary, when two straight wires are parallel to each other and carry different currents in the same direction, they will attract each other with equal forces determined by the formula F = (2 X 10-7/r) I1I2L2. This is because the magnetic fields generated between the wires will point in opposite directions, resulting in attraction. The magnitudes of these forces are equal, as determined by the force equations derived.
  • #1
predentalgirl1
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1
Magnetic Forces on Current-Carrying Wires (Conceptual Question)...Is answer correct?

Two straight wires are parallel to each other and carry different currents in the same direction. Do they attract or repel each other? How do the magnitudes of these forces on each wire compare?






The formula used to calculate these attractive or repulsive forces is:



F = BIL

F12 = (μ0I1/2πr)I2L2

F12 = (μ0/2πr) I1I2L2

F12 = (4π X 10-7/2πr) I1I2L2

F12 = (2 X 10-7/r) I1I2L2

F12 represents the force on wire 2 caused by its presence in the magnetic field of wire 1

I1 is the current flowing in wire 1

I2 is the current flowing in wire 2

L2 is the length of the current segment of wire 2 in the field of wire 1

r is the distance between the wires

F21 represents the force on wire 1 caused by its presence in the magnetic field of wire 2

F21 = (μ0I2/2πr)I1L1

F21 = (μ0/2πr) I1I2L1

F21 = (4π X 10-7/2πr) I1I2L1

F21 = (2 X 10-7/r) I1I2L1





3. Answer

If two current carrying wires are parallel to each other, their respective magnetic fields either attract or repel each other.



If two parallel wires have currents traveling in the same direction, the magnetic fields generated by those currents between the wires will both point in opposite directions resulting in the wires attracting each other.

If two parallel wires have currents traveling in opposite directions, the magnetic fields generated by those currents between the wires will both point in the same direction, in this case, into the plane of the page. These wires would repel each other.



 
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  • #2
Thats a very good explanation. So how do the magnitudes compare and do they attract or repel?
 
  • #3
Kurdt said:
Thats a very good explanation. So how do the magnitudes compare and do they attract or repel?

How do they compare? I'm not sure..
 
  • #4
Well you've pretty much worked them out. The magnitude just means the number associated with it and disregarding the direction. What can you say about the two force equations you've derived?
 
  • #5
Kurdt said:
Well you've pretty much worked them out. The magnitude just means the number associated with it and disregarding the direction. What can you say about the two force equations you've derived?

Forces are equal (equal magnitude). And parallel currents attract each other.
 
  • #6
predentalgirl1 said:
Forces are equal (equal magnitude). And parallel currents attract each other.

Very good.
 

Related to Magnetic Forces on Current-Carrying Wires: Attraction & Repulsion

1. What is the relationship between magnetic fields and current-carrying wires?

The flow of electric current through a wire creates a magnetic field around the wire. This magnetic field interacts with other magnetic fields in the surrounding area, causing attraction or repulsion between the wires.

2. How does the direction of current affect the magnetic forces on a wire?

The direction of the current in a wire determines the direction of the magnetic field around the wire. When two current-carrying wires are parallel and have the same direction of current, they will experience a repulsive force. If the currents are in opposite directions, the wires will be attracted to each other.

3. What is the difference between attraction and repulsion in magnetic forces?

Attraction occurs when the currents in two parallel wires are in opposite directions, creating magnetic fields that are attracted to each other. Repulsion occurs when the currents are in the same direction, causing the magnetic fields to repel each other.

4. How can the strength of the magnetic force on a wire be increased?

The strength of the magnetic force on a wire can be increased by increasing the current flowing through the wire or by increasing the distance between the wires. Additionally, using a stronger magnet or increasing the number of turns in the wire can also increase the magnetic force.

5. What are some real-world applications of magnetic forces on current-carrying wires?

Magnetic forces on current-carrying wires are used in a variety of applications, including electric motors, generators, and transformers. They are also used in technologies such as MRI machines and maglev trains. Additionally, they are essential in the production of electricity through hydroelectric power plants.

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