# Magnetic force on a current carrying wire looped into a solenoid

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.

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

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.

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