- #1
ShizukaSm
- 85
- 0
Frequently, when a length is bigger than another (say, an axial distance is bigger than the radius of something related) a certain assumption is made and the smaller length is "removed" from a formula. It's hard to describe, so let me show an example:
The magnetic field from a bobbin at an axial distance Z is:
[itex]B = \frac{\mu_0 i R^2}{2(R^2+z^2)^{3/2}}[/itex]
But, according to my book, when [itex] z \gg R [/itex]:
[itex]B = \frac{\mu_0 i R^2}{2z^3}[/itex]
Even though this is just an example I've seen similar assumptions being made multiple times. How do I arrive at such conclusion? I hardly think that I must simply "delete" the smaller length ([itex]R^2[/itex]) in the example, surely there must be a procedure to conclude that precisely?
The magnetic field from a bobbin at an axial distance Z is:
[itex]B = \frac{\mu_0 i R^2}{2(R^2+z^2)^{3/2}}[/itex]
But, according to my book, when [itex] z \gg R [/itex]:
[itex]B = \frac{\mu_0 i R^2}{2z^3}[/itex]
Even though this is just an example I've seen similar assumptions being made multiple times. How do I arrive at such conclusion? I hardly think that I must simply "delete" the smaller length ([itex]R^2[/itex]) in the example, surely there must be a procedure to conclude that precisely?