en.wikipedia.org/wiki/Coilgun

This date is not just unsupported; it is chronologically impossible.

• Kristian Birkeland was born in 1867, so he could not have started developing a coilgun in 1845, 22 years before his birth.
• The Nobel Prize nomination archive lists Birkeland's birth year as 1867.
• The Norwegian Museum of Science and Technology states that in 1901 Birkeland got the idea for the electromagnetic cannon: "I 1901 fikk Kristian Birkeland en idé ..." ("In 1901 Kristian Birkeland got an idea ...").
• Birkeland's U.S. patent for the electromagnetic gun was filed on January 2, 1902 and published/granted on March 15, 1904, which fits a development timeline around 1901–1902, not 1845.

So the year 1845 is an error, very likely a typo for a much later date.

The statement says that vacuum permeability is defined in SI units as exactly (4\pi \times 10^{-7}). That used to be true under the old SI, but it is no longer correct after the SI redefinition that took effect on May 20, 2019.

• NIST explains that, with the revised SI and redefinition of the ampere, “the permeability of vacuum will not have a fixed numerical value but will become, in principle, a measurable quantity.”
• The BIPM's 2018 CGPM resolution states that from 20 May 2019, the vacuum magnetic permeability (\mu_0) equals (4\pi \times 10^{-7},\mathrm{H,m^{-1}}) with a relative uncertainty, and that “in the future, its value will be determined experimentally.”

So the exact wording "defined in SI units as" is incorrect for the current SI. A correct modern phrasing would be that (\mu_0) is approximately (4\pi \times 10^{-7},\mathrm{H/m}), not an exactly defined SI value.