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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.

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  • $\begingroup$ 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

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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.

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  • $\begingroup$ 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

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