0

$A, B$ are constants with unknown units.

$n$ is an unknown integer.

I have the following:

len is quantity for length

$A \cdot (len)^2 + B$ represent electric potential.

$A \cdot (len)^{n-5}$ it's also represent electric potential.

In my exercise, I know that those expressions are represent the same electric potential(electric potential is continuous function).

Can I tell for sure that $n=7$?

Thanks.

Asaf
  • 131

1 Answers1

0

Yes. It does not matter what they are, just that they have the same units. As long as the units match between the two expressions, you are given that $[m^2]=[m^{n-5}],$ which tells you that $n-5=2$

Ross Millikan
  • 374,822
  • Why I don't need to concern about $B$? – Asaf Dec 14 '19 at 16:41
  • 1
    When you add things they have to have the same units, so $B$ doesn't add anything to the problem. You know its units are $m^2$ times the units of $A$, but that is not useful here. – Ross Millikan Dec 14 '19 at 17:30