Correction to: Scientific Reports https://doi.org/10.1038/s41598-024-77883-9, published online 03 December 2024

The original version of this Article contained an error in Eq. 7.

$$r=\frac{{B}_{g}{u}_{ano}z{q}_{e}\text{ sin} \, \varphi }{\beta \omega }\text{cos} \, \omega t+\frac{{B}_{g}{u}_{ave}z{q}_{e}\text{ sin} \,\varphi }{\beta \omega }$$

now reads:

$$r=\frac{{B}_{g}{u}_{ano}z{q}_{e}\text{ sin} \, \varphi }{\beta \omega }\text{cos} \, \omega t+\frac{{B}_{g}{u}_{ano}z{q}_{e}\text{ sin} \, \varphi }{\beta \omega }$$

The original Article has been corrected.