Finding Vector Potential of Infinite Solenoid

In summary, the conversation is about finding the Vector Potential of an infinite solenoid with n turns per unit length, radius R, and current I. The suggested method involves using the equation for vector potential and Stoke's theorem, with a closed curve chosen suitably. Another helpful suggestion is to use the fact that the line integral of A around a closed path is equal to the flux of B through the path. At internal points, B is equal to (n)(I)/((eps0)(c^2)) for an infinitely long solenoid, and 0 at all points outside the solenoid. Finally, an equation for A is provided for a distance r>R from the solenoid's axis.
  • #1
heman
361
0
How to find the Vector Potential of an infinite solenoid with n turns per unit length,radius R and current I.
since here current extends to infinty..
How will it be done
Pls Help
 
Physics news on Phys.org
  • #2
Heman, please try to write the equation for vector potential. Then we can better point you in the right direction.

You can use LateX - see the thread on Math applications of LateX - https://www.physicsforums.com/showthread.php?t=8997 (General physics forum).
 
  • #3
The infinite solenoid has a uniform magnetic field parallel to the solenoid axis. Let that axis be the z axis, for concreteness. So [itex]\mathbf {B}=B \mathbf {k}[/itex]. Now the vector potential is [itex]\mathbf {B}=\nabla \times \mathbf {A}[/itex]. The vector potential is not unique, so any vector-valued function [itex]\mathbf {A}[/itex] whose curl gives you [itex]B \mathbf{k}[/itex] will fit the bill.
 
  • #4
You may consider using the following:
gradXA = B
then use Stoke's theorem to write surface int(gradXA.dS) = line int (A.dl), with the closed curve chosen suitably.

This gives line int(A.dl) = int(B.ds).

The surface integral is straight forward while a reasonable choic eof the closed curve makes the line integral staright forward.

Of help?
 
  • #5
heman said:
How to find the Vector Potential of an infinite solenoid with n turns per unit length,radius R and current I.
since here current extends to infinty..
How will it be done
Pls Help

The line integral of A around a closed path is equal to the flux of B through the path. For an infinitely long solenoid, B = (n)(I)/((eps0)(c^2)) at internal points. (B = 0 at all points outside of the solenoid.) Thus the flux of B inside the solenoid is (pi)(R^2)(n)(I)/((eps0)(c^2)). At a distance r>R from the solenoid's axis, (2)(pi)(r)(A)=flux of B. That is,

A=(n)(I)(R^2)/((2)(eps0)(c^2)(r))
 
  • #6
jimmy neutron said:
Of help?

I don't think so. In fact the thread is 5 years old. It might be of help for further people though.
 

1. What is a vector potential?

A vector potential is a mathematical quantity used to describe the direction and magnitude of a magnetic field. It is a vector field that represents the magnetic potential energy of a system.

2. What is an infinite solenoid?

An infinite solenoid is a theoretical construct that consists of a long, infinitely thin wire wrapped in a helical shape. It has a uniform magnetic field inside that extends infinitely and zero field outside.

3. Why is it important to find the vector potential of an infinite solenoid?

Finding the vector potential of an infinite solenoid allows us to understand the behavior of magnetic fields in this type of system. It is also a useful tool for calculating the magnetic field strength and direction at any point inside or outside the solenoid.

4. What is the process for finding the vector potential of an infinite solenoid?

The process involves using the Biot-Savart law, which describes the magnetic field created by a current-carrying wire, to calculate the magnetic vector potential at any point. The integral form of the Biot-Savart law is used for an infinitely long wire, and it involves integrating over the length of the solenoid.

5. Are there any practical applications for the vector potential of an infinite solenoid?

Yes, the vector potential of an infinite solenoid is used in many practical applications, such as in the design of magnetic devices like MRI machines and particle accelerators. It is also used in electromagnetic theory to understand the behavior of magnetic fields in various systems.

Similar threads

Replies
1
Views
642
  • Mechanics
Replies
10
Views
3K
Replies
5
Views
1K
  • Electromagnetism
Replies
2
Views
878
  • Introductory Physics Homework Help
Replies
7
Views
724
Replies
2
Views
198
Replies
10
Views
901
  • Advanced Physics Homework Help
Replies
1
Views
595
  • Electrical Engineering
Replies
1
Views
738
Replies
5
Views
4K
Back
Top