Confusion on the magnitude of magnetic fields

In summary: Please write a summary and explain with as much detail as possible how do you apply Ampere's law for this system so that you infer that ##B_y=B_x=B_z=0## for the interior of the pipe. ##B_x## and ##B_z## are indeed zero but not ##B_y##.
  • #1
Gourab_chill
55
3
Homework Statement
I've put question below.
Relevant Equations
B=µNI; N=no of turns for unit length of solenoid
Capture.PNG

Here, the correct options are A,D.
Solution:
Capture1.PNG

I got A as answer as ∫ B.dl=µI. But, the answer to the question says that it is a solenoid and therefore Bx=0 for point P. Here I'm a bit confused. I know this system resembles a solenoid in some ways, then By must have some finite value, but ampere's law says there should be no magnetic field in the pipe or it's magnitude is zero. Where am I mistaking?
 
Physics news on Phys.org
  • #2
I believe you are applying Ampere's law wrongly in the interior of the pipe (probably because you are misconceiving the symmetries present in this system). From Ampere's law we can't deduce that the B-field will be zero inside, not for this system. If the pipe was doing only translational motion then we could deduce that the B-field would be zero inside but because it does rotational motion too around the y-axis, it generates a component ##B_y## in the interior that it isn't zero.
 
  • Like
Likes etotheipi
  • #3
Delta2 said:
I believe you are applying Ampere's law wrongly in the interior of the pipe (probably because you are misconceiving the symmetries present in this system). From Ampere's law we can't deduce that the B-field will be zero inside, not for this system. If the pipe was doing only translational motion then we could deduce that the B-field would be zero inside but because it does rotational motion too, it generates a component ##B_y## in the interior that it isn't zero.
So, where is exactly ampere's law applicable? If the current is moving around the pipe (due to rotational motion as here), we cannot apply it? Does the current have to be perpendicular to the imaginary circle we consider in ampere's law?
 
  • #4
Ampere's law is applicable everywhere, I just meant that you apply the law in the wrong way for this system.
Please write a post and explain with as much detail as possible how do you apply Ampere's law for this system so that you infer that ##B_y=B_x=B_z=0## for the interior of the pipe. ##B_x## and ##B_z## are indeed zero but not ##B_y##.
 
  • #5
Delta2 said:
Ampere's law is applicable everywhere, I just meant that you apply the law in the wrong way for this system.
Please write a post and explain with as much detail as possible how do you apply Ampere's law for this system so that you infer that ##B_y=B_x=B_z=0## for the interior of the pipe. ##B_x## and ##B_z## are indeed zero but not ##B_y##.
All I knew till now is that by applying ampere's law the net magnetic field at a point is zero if it does not encloses any current.
For solenoids as I looked up, the derivation also uses ampere's law, however here the loop encloses current due to it's position which I've tried to show in the first figure. What if we take the loop as in the second figure? The magnetic field should be zero in the second case or is the loop position wrong?
Untitled.png
 
  • #6
lets focus on the second case. Assume that the B-field has a ##B_y## component (y the axis of the pipe). Do we get any info for this ##B_y## component by applying Ampere's law for the loop shown in the second case? NO we don't because ##B_y## is always perpendicular to the ##dl## of the loop (since the loop lies in the x-z plane) so it is ##\vec{B_y}\cdot \vec{dl}=0## because the dot product is always zero as long as the vectors are perpendicular to each other. ##B_y## might be zero or might be any other value but because its dot product will be zero (for this specific loop we choose to apply the law), amperes law hold. That is Ampere's law hold for any choice of ##B_y## for this specific loop.

If we choose the loop of the first case, then we can extract useful info about ##B_y## (because it is not perpendicular everywhere , it is in the same direction as ##dl## in the segments of the loop that are along the y-axis) by applying ampere's law for this loop.
 
  • Like
Likes Gourab_chill
  • #7
Delta2 said:
lets focus on the second case. Assume that the B-field has a ##B_y## component (y the axis of the pipe). Do we get any info for this ##B_y## component by applying Ampere's law for the loop shown in the second case? NO we don't because ##B_y## is always perpendicular to the ##dl## of the loop (since the loop lies in the x-z plane) so it is ##\vec{B_y}\cdot \vec{dl}=0## because the dot product is always zero as long as the vectors are perpendicular to each other. ##B_y## might be zero or might be any other value but because its dot product will be zero (for this specific loop we choose to apply the law), amperes law hold. That is Ampere's law hold for any choice of ##B_y## for this specific loop.

If we choose the loop of the first case, then we can extract useful info about ##B_y## (because it is not perpendicular everywhere , it is in the same direction as ##dl## in the segments of the loop that are along the y-axis) by applying ampere's law for this loop.
Thanks :)
 

Related to Confusion on the magnitude of magnetic fields

1. What is the difference between magnetic field strength and magnetic field intensity?

Magnetic field strength refers to the amount of force that a magnetic field exerts on a charged particle, while magnetic field intensity refers to the density of the magnetic field lines in a given area.

2. How is the magnitude of a magnetic field measured?

The magnitude of a magnetic field is typically measured in units of Tesla (T) or Gauss (G) using a device called a magnetometer.

3. Can the magnitude of a magnetic field vary in different locations?

Yes, the magnitude of a magnetic field can vary depending on the location and the source of the magnetic field. For example, the Earth's magnetic field is stronger at the poles than at the equator.

4. What factors can affect the magnitude of a magnetic field?

The magnitude of a magnetic field can be affected by the strength and orientation of the magnetic source, as well as the distance from the source and any intervening materials that may alter the field.

5. How does the magnitude of a magnetic field impact its effects on objects?

The magnitude of a magnetic field can impact the strength of its effects on objects, such as the force it exerts on charged particles or the degree to which it can influence the direction of a compass needle.

Similar threads

  • Introductory Physics Homework Help
Replies
7
Views
198
Replies
2
Views
170
  • Introductory Physics Homework Help
Replies
5
Views
782
  • Introductory Physics Homework Help
Replies
7
Views
306
  • Introductory Physics Homework Help
Replies
2
Views
1K
  • Introductory Physics Homework Help
Replies
11
Views
2K
  • Introductory Physics Homework Help
Replies
1
Views
432
  • Introductory Physics Homework Help
Replies
4
Views
968
  • Introductory Physics Homework Help
Replies
3
Views
2K
  • Introductory Physics Homework Help
Replies
5
Views
1K
Back
Top