2
$\begingroup$

I am having a bit of trouble understanding a very basic concept, which is the following. If inside a solenoid, there is no current going through (since it goes through the wires making up the structure), how can there be a magnetic field inside? I have seen the proof both through Biot-Savart and Ampère's Law, but in both cases I am failing to understand the physical interpretation.

All help is really appreciated.

Improve this question
$\endgroup$
1
  • 1
    $\begingroup$ Why is this a problem? There is no current going through a point outside a current carrying wire, but there is a magnetic field... $\endgroup$
    – ProfRob
    Commented Nov 30, 2017 at 12:23

1 Answer 1

Reset to default
0
$\begingroup$

The relationship between magnetic field and current (in magnetostatics) is only that the curl of the magnetic field is proportional to the current density at that point. $$ \nabla \times {\bf B} = \mu_0\ {\bf J}$$ There is no relationship between the B-field itself at some point in space and the current found at that position.

Improve this answer
$\endgroup$
7
  • $\begingroup$ About your comment, I see that if we have a wire with current through it, we can take an Amperian loop around it and then some current will be crossing our surface limited by the loop. However, in this case, I can take a circular loop INSIDE the solenoid, and no current would be punching through the surface (or current density), right? $\endgroup$
    – Bee
    Commented Nov 30, 2017 at 12:36
  • $\begingroup$ @Bee, I think you have the incorrect impression that if an Amperian loop is zero, there is zero magnetic field present. This isn't true. Consider, for example, all the undergraduate E&M problems that begin with "assume a uniform magnetic field". Ampere's law says that if the closed contour integral of $\vec B \cdot d\vec l$ is non-zero, there is a current through the surface bounded by the contour. If there's no current through, the integral is zero but this doesn't imply zero magnetic field. $\endgroup$
    – Alfred Centauri
    Commented Nov 30, 2017 at 13:03
  • $\begingroup$ @Bee Or indeed zero curl, which is what my answer says. Besides which, why do you get to choose which loop to use in the case of the wire, but not the solenoid? I could choose to put a closed loop in space outside the wire; that has no current going through it, but there is still a magnetic field. Conversely, I could choose a loop that starts in the solenoid and goes outside the solenoid. That does have a current going through it. $\endgroup$
    – ProfRob
    Commented Nov 30, 2017 at 13:27
  • $\begingroup$ Thank you both very much. I think I am starting to get an idea of what you mean, but to be honest, my professor has not explained Ampère's Law this way, so I would really appreciate it if you could provide me with some internet sources to read more about it. I am concerned about knowing how to choose the loop: in the case of the wire, I automatically think of choosing the loop which is centered around the wire. But in the case of the solenoid, the loop you described is not the first thing that comes to my mind. $\endgroup$
    – Bee
    Commented Nov 30, 2017 at 21:52
  • $\begingroup$ @Bee the loop I describe is exactly how you calculate the B-field in a solenoid. Ampere's law is covered in every electromagnetism textbook. $\endgroup$
    – ProfRob
    Commented Nov 30, 2017 at 22:09

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.

Not the answer you're looking for? Browse other questions tagged or ask your own question.