How would you find the lorentz force on a current-carrying wire that is looped into a solenoid?

As a followup question:

How could one use the amount of force calculated to determine whether a wire will be able to hold to those forces.

  • $\begingroup$ What do you mean by looped in a solenoid? $\endgroup$
    – Kashmiri
    Oct 14, 2020 at 2:43
  • $\begingroup$ @Yasir Sadiq I was just referring to when you coil up a wire into a solenoid. $\endgroup$
    – dl19
    Oct 14, 2020 at 20:40
  • $\begingroup$ Have you searched for 'magnetic force'? $\endgroup$
    – my2cts
    Apr 10, 2022 at 0:08

1 Answer 1


in an ideal solenoid the magnetic field is constant and the equation of the magnetic field is given as $\vec{B}=\mu_{0} n I_{1}$.

The force on the loop wire is given as $\vec{F}=I_{2} \oint \vec{d} l \times \vec{B}$ ,since $B$ is constant it'll come out of the integral, hence

$\vec{F}=I_{2}(\oint \overrightarrow{d l}) \times \vec{B}$

But $\oint \overrightarrow{d l}=0$ since the total displacement is zero,

$\Rightarrow \vec{F}=0$.

So the total force on the wire is zero however the wire will have tension in it due to the stretch on the wire.

  • $\begingroup$ What do you mean by tension? Would adding current cause the wire to stretch? $\endgroup$
    – dl19
    Oct 17, 2020 at 21:46
  • $\begingroup$ Yes it can lead to stretch or shrink due to magnetic force on the charges moving inside the wire. See Lorentz Force. $\endgroup$
    – Kashmiri
    Oct 18, 2020 at 10:58
  • $\begingroup$ How could I calculate this tension in order to determine the resulting structural integrity of the wire in the solenoid? $\endgroup$
    – dl19
    Oct 19, 2020 at 2:18
  • $\begingroup$ There is some discssion of the forces on solenoiud magnets in en.wikipedia.org/wiki/Bitter_electromagnet. $\endgroup$
    – mike stone
    Apr 9, 2022 at 13:05

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.