Answer
$L = 1.4~cm$
Work Step by Step
We can find the magnetic moment:
$B = \frac{\mu_0~\mu}{2\pi~r^3}$
$\mu = \frac{2\pi~r^3~B}{\mu_0}$
$\mu = \frac{(2\pi)~(0.50~m)^3~(7.5\times 10^{-9}~T)}{4\pi\times 10^{-7}~T~m/A}$
$\mu = 0.0046875~A~m^2$
We can find the length $L$ of each side of the square:
$\mu = I~A$
$\mu = I~L^2$
$L^2 = \frac{\mu}{I}$
$L = \sqrt{\frac{\mu}{I}}$
$L = \sqrt{\frac{0.0046875~A~m^2}{25~A}}$
$L = 0.014~m$
$L = 1.4~cm$
