Question: atomic polarizability (Purcell book)

[bobfei]

Hi All,

I would like to ask a question on Purcell’s EM textbook on atomic polarizability.

On page 362, Purcell put the relation:

$$\underbrace {\frac{{\Delta z}}{a}}_{{\rm{dimensionless}}} \approx \underbrace {\frac{E}{{e/{a^2}}}}_{\frac{1}{{{\varepsilon _0}}}}$$


I suspect that it has missed the constant $${\varepsilon _0}$$ here. The left side of the approximate equation is a dimensionless quantity, whereas on the right side:

E has dimension $$\frac{e}{{{\varepsilon _0}{a^2}}}$$, dividing by the denominator, the net result will still have the dimension of $$\frac{1}{{{\varepsilon _0}}}$$.

But why Purcell put the equation like that? I also compared with Griffiths book as well as Wikipedia, both of which gave the correct dimension. So Purcell must be wrong here, but why he makes such a junior level mistake?

Thanks,
Bob

 

[issacnewton]

I think Purcell is using CGS Electrostatic units.

check

http://en.wikipedia.org/wiki/Centimetre_gram_second_system_of_units

Edit:Griffiths uses SI system . So it makes sense...

 

[bobfei]

I think this makes sense, thanks for the answer.

Bob