Cylindrically symmetric current distribution: Magnetic field in all space

In summary, for an infinite cyclindrically symmetric current distribution with the given forms, we can use the Biot-Savart law and Ampere's law to calculate the magnetic field everywhere in space. For part a, where the current is only in the phi direction, Ampere's law can be used to determine the magnetic field outside the interval where the current is 0. Similarly, for part b, where the current is only in the z direction, Ampere's law can be used to determine the magnetic field outside the interval where the current is 0.
  • #1
JamesTheBond
18
0

Homework Statement



a. An infinite cyclindrically symmetric current distribution has the form
[tex]\vec J (r, \phi, z) = J_0 r^2/R^2 \ \ \ \vec\hat \phi[/tex] for [tex]R<r<2R[/tex]. Outside the interval, the current is 0. What is the field everywhere in space?

b. An infinite cyclindrically symmetric current distribution has the form
[tex]\vec J (r, \phi, z) = J_0 r^2/R^2 \ \ \ \vec \hat z [/tex] for [tex]R<r<2R[/tex]. Outside the interval, the current is 0. What is the field everywhere in space?




Homework Equations



Ampere's Law
Biot Savart?


The Attempt at a Solution



r<R B = 0

r>2R B= 0

?

I don't know where to start.
 
Last edited:
Physics news on Phys.org
  • #2
Can someone help me?


Hello, thank you for your post. It seems like you are on the right track with considering the regions where the current is 0. To solve for the magnetic field everywhere in space, you will need to use the Biot-Savart law and Ampere's law. The Biot-Savart law allows us to calculate the magnetic field at a point due to a current element, while Ampere's law relates the magnetic field around a closed loop to the current enclosed by that loop.

For part a, since the current is only in the phi direction, you can use the Biot-Savart law to calculate the magnetic field at a point (r, phi, z) due to the current distribution. Then, use Ampere's law to determine the magnetic field outside the interval where the current is 0.

For part b, since the current is only in the z direction, you can use the Biot-Savart law to calculate the magnetic field at a point (r, phi, z) due to the current distribution. Then, use Ampere's law to determine the magnetic field outside the interval where the current is 0.

I hope this helps guide you towards a solution. Let me know if you have any further questions. Good luck with your problem!
 
  • #3
Can you please provide more information about the problem? What is the physical situation and what are we trying to solve for? Also, it would be helpful to have any relevant equations or concepts to use. Without this information, it is difficult to provide a meaningful response.
 

1. What is a cylindrically symmetric current distribution?

A cylindrically symmetric current distribution is a type of current flow where the current is evenly distributed throughout a cylindrical volume. This means that the magnitude and direction of the current are the same at all points along the cylinder's length.

2. What is the significance of a cylindrically symmetric current distribution?

Cylindrically symmetric current distributions are important in many areas of physics and engineering, as they are commonly found in practical applications such as electromagnets, motors, and generators. They also have analytical solutions that can be used to model and understand more complex current distributions.

3. How does a cylindrically symmetric current distribution affect the magnetic field in all space?

A cylindrically symmetric current distribution produces a magnetic field that is also cylindrically symmetric, meaning it has the same magnitude and direction at all points along the length of the cylinder. The strength of the magnetic field decreases as you move further away from the cylinder, following an inverse-square law.

4. What is the mathematical equation for the magnetic field of a cylindrically symmetric current distribution?

The magnetic field at any point in space due to a cylindrically symmetric current distribution can be calculated using the Biot-Savart Law, which states that the magnetic field at a point is directly proportional to the current and the vector cross product of the current element and the distance from the point. The equation is B = μ0I/(2πr), where μ0 is the permeability of free space, I is the current, and r is the distance from the current element.

5. How can we use the magnetic field of a cylindrically symmetric current distribution in practical applications?

The magnetic field produced by a cylindrically symmetric current distribution can be harnessed for various applications, such as in MRI machines, particle accelerators, and magnetic levitation systems. Understanding and controlling the magnetic field of a cylindrically symmetric current distribution is essential for designing and optimizing these technologies.

Similar threads

  • Introductory Physics Homework Help
Replies
3
Views
924
  • Introductory Physics Homework Help
Replies
17
Views
278
  • Introductory Physics Homework Help
Replies
25
Views
160
  • Introductory Physics Homework Help
Replies
5
Views
191
  • Introductory Physics Homework Help
Replies
7
Views
99
  • Introductory Physics Homework Help
Replies
6
Views
894
  • Introductory Physics Homework Help
Replies
2
Views
195
  • Introductory Physics Homework Help
Replies
7
Views
768
  • Introductory Physics Homework Help
Replies
7
Views
1K
  • Introductory Physics Homework Help
Replies
3
Views
740
Back
Top