Dimensional analysis of the london penetration depth

1. May 25, 2010

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.

2. May 27, 2010

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!