# Do charge carriers in a current carrying wire experience a magnetic force due to the net magnetic field "they create"

I know this sounds like a bit of a stupid question and it low key is.

But I know that the magnetic force due to a current carrying wire of radius $$R$$ at a distance $$r$$ from the central axis of the wire is given by: $$\vec{B}=\frac{\mu_0 i}{2\pi}\frac{r}{R^2}\hat{e_{\theta}}$$

When $$r\leq R$$.

Now I'm wondering if this magnetic field causes the charger carriers within the wire to experience a magnetic force due to this created magnetic field.

I know for an individual charge in a reference frame where the magnetic field due to that moving charge is present, it does not experience a force due to its own magnetic field. But since this magnetic field($$\vec{B}=\frac{\mu_0 i}{2\pi}\frac{r}{R^2}\hat{e_{\theta}}$$) is the result of many charge carriers would this magnetic field have an effect on the charge carriers of the wire?

Using an oversimplified model of a current carrying wire. If the charge carriers DID experience a force due to this field. It would cause them to move helically through the wire.

Now I know ultimately I know this question is slightly redundant since a charge carrying wire isn't nearly as simple as a stream of point charges moving at a constant velocity $$\perp$$ to $$B$$.

But still it has been something I've been quite curious about for awhile and I did not find any answers on Google.

Kind Regards.

• You might be interested in Googling ‘magnetically insulated transmission line’. Nov 24, 2022 at 3:27
• see im google the simple solutions to "two electrons moving parallel to each other at same velocity" Nov 24, 2022 at 5:10
• I cannot write an answer, but if one looks at the microscopic view of current (hyperphysics.phy-astr.gsu.edu/hbase/electric/miccur.html ) and thinks and assumes the drift velocity for each carrier, then there will be an effect as seen in the solutions in the search statement I gave before,. Nov 24, 2022 at 5:24
• For "two electrons moving parallel to each other at same velocity" referred in a comment by @anna v see my answer here Charges and relative motion. Nov 24, 2022 at 8:21
• Nov 24, 2022 at 8:24

As given in the answers to Magnetic force in the inside of cylindrical conductor? and Pressure experienced due to magnetic force?, the radial magnetic pressure at a radius $$r$$ inside a straight cylindrical conductor of external radius $$R$$ carrying a current $$I$$ is $$P=\frac{\mu I^2r^2}{8\pi^2 R^4}$$