Vector Potential Between Parallel Wires: Calculating & Differences

In summary, the vector potential between parallel wires is a measure of the magnetic field produced by current flowing through the wires. It can be calculated using the Biot-Savart law and is found by taking the curl of the magnetic field. While the magnetic field is a physical quantity, the vector potential is a mathematical tool with no direct physical interpretation. The vector potential is dependent on the current and distance between the wires and its direction depends on the wire orientation. It is important in various fields such as electromagnets, circuit design, and particle physics.
  • #1
galipop
51
0
Hi All,

I've just looked at an example for calculating the vector potential for a point in the vicinity of a long straight wire.

I've now got to calculate the vector potential for a point between 2 parallel straight wires carrying currents in opposite directions. How does the vector potential differ in this case.

By the way...study biot-savart is giving me a headache :)
 
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  • #2
does anyone want to have a crack at it?
 
  • #3
I would think you just add them together (with the appropriate sign).
 

What is the vector potential between parallel wires?

The vector potential between parallel wires is a measure of the magnetic field produced by the current flowing through the wires. It is a vector quantity that describes the direction and magnitude of the magnetic field at any point in space.

How do you calculate the vector potential between parallel wires?

The vector potential between parallel wires can be calculated using the Biot-Savart law, which states that the magnetic field at a point is directly proportional to the current flowing through the wire and inversely proportional to the distance from the wire. The vector potential is then found by taking the curl of the magnetic field.

What are the differences between the vector potential and the magnetic field?

The magnetic field is a vector quantity that describes the force experienced by a charged particle in a magnetic field. The vector potential, on the other hand, is a mathematical tool used to calculate the magnetic field. It is not a physical quantity and does not have a direct physical interpretation. Additionally, while the magnetic field is a vector quantity, the vector potential is a pseudovector quantity, meaning that it behaves differently under certain transformations.

How does the vector potential change with different configurations of parallel wires?

The vector potential is dependent on the current flowing through the wires and the distance between the wires. As the current or distance changes, the vector potential will also change. Additionally, the direction of the vector potential will depend on the orientation of the wires with respect to each other.

What are the practical applications of understanding the vector potential between parallel wires?

Understanding the vector potential between parallel wires is important in many areas of science and engineering. It is used to calculate the magnetic field in devices such as electromagnets, motors, and generators. It is also used in the design and optimization of circuits and in studies of electromagnetic interference. Additionally, the vector potential is essential in understanding the behavior of charged particles in magnetic fields, which has applications in particle accelerators and plasma physics.

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