Answer
$L = 1.4\times 10^{-3}~H$
Work Step by Step
We can find the inductance:
$I_L = \frac{V_L}{\omega ~L}$
$L = \frac{V_L}{\omega ~I_L}$
$L = \frac{V_L}{2\pi ~f ~I_L}$
$L = \frac{\sqrt{2}~V_{rms}}{2\pi ~f ~I_L}$
$L = \frac{(\sqrt{2})(6.0~V)}{(2\pi) (15\times 10^3~Hz) ~(65\times 10^{-3}~A)}$
$L = 1.4\times 10^{-3}~H$
