Dimensional analysis of the london penetration depth

[phja]

hi guys.

i have the london penetration depth defined as $$\lambda_l = \sqrt{\frac{m^{**}}{4\pi n_{s} e^{2}}}$$.

i'm trying to figure out the dimensionality of it...surely it must be a length, but i get

$$[(Kg)(m^{3})(A^{-1}s^{-1})]^{0.5}$$

in SI units.

am i doing something wrong?

cheers.

 

[xepma]

There are some units set to '1' in this expression, which is why your analysis comes out funky. You will need some factors of c or $$\mu_0$$ in your expression for the depth to make the dimension come out correct.

You could try to re-derive the expression for the depth yourself (just google it), and use the expression for the Maxwell equation with the proper units in place. It's doable!