Why am I getting two different results in emu and SI unit?

[faheemahmed6000]

I am computing force between two magnetic poles each of one unit pole (in emu) and situated one centimeter apart.

In electromagnetic units:
$F_{dyne}=\dfrac{p^2}{r_{cm}^2}=\dfrac{1^2}{1^2}=1 dyne$
where $p$ is pole strength in emu

In SI units:
$F_{N}=k_A \dfrac{P^2}{r_m^2}=10^{-7} \dfrac{({1.25\times 10^{-7}})^2}{10^{-4}}=1.5625 \times 10^{-17} \neq 10^{-5}N=1dyne$
where $P$ is that same pole strength in SI units

with $P=1.25\times10^{-7}p$ (see here)

Now why am I getting two different results in emu and SI for the same configuration?

 

[mfb]

The units in the formula "in SI units" don't match, at least not if k_a is supposed to be $\frac{\mu_0}{4 \pi}$ as the numerical value used for it would suggest.
Working with units helps to spot errors.

 

[faheemahmed6000]

The units in the formula "in SI units" don't match, at least not if k_a is supposed to be $\frac{\mu_0}{4 \pi}$ as the numerical value used for it would suggest.
Working with units helps to spot errors.

Please can you explain a bit more elaborately?

 

[mfb]

Work with units, then the problem will become clear.

 

[Dale]

In electromagnetic units:
$F_{dyne}=\dfrac{p^2}{r_{cm}^2}=\dfrac{1^2}{1^2}=1 dyne$
where $p$ is pole strength in emu

I agree with @mfb. You need to show the units in each of your intermediate steps. As it is, I can tell that F is in dyne and r is in cm, but I cannot tell if p is in abC or statC. If it is abC then your equation is wrong, and if it is in statC then you are using electrostatic units not electromagnetic units.

 

[Wrichik Basu]

@faheemahmed6000 one question: did you also post this in Physics Stack Exchange?