Answer
$L = 2.0\times 10^{-3}~H$
$C = 1.3\times 10^{-7}~F$
Work Step by Step
We can use the energy to find the required inductance:
$E = \frac{1}{2}LI^2$
$L = \frac{2E}{I^2}$
$L = \frac{(2)(1.0\times 10^{-5}~J)}{(0.10~A)^2}$
$L = 2.0\times 10^{-3}~H$
We can find the required capacitance:
$f = \frac{1}{2\pi~\sqrt{LC}}$
$f^2 = \frac{1}{4\pi^2~LC}$
$C = \frac{1}{4\pi^2~L~f^2}$
$C = \frac{1}{(4\pi^2)~(2.0\times 10^{-3}~H)~(10\times 10^3~Hz)^2}$
$C = 1.3\times 10^{-7}~F$
