Answer
The energy stored in the magnetic field is $~~5.10~J$
Work Step by Step
We can find the current at $t = 2.00~s$:
$i = \frac{\mathscr{E}}{R}~(1-e^{-tR/L})$
$i = \frac{10.0~V}{6.70~\Omega}~[1-e^{-(2.00~s)(6.70~\Omega)/(5.50~H)}]$
$i = 1.362~A$
We can find the energy stored in the magnetic field:
$U_B = \frac{i^2~L}{2}$
$U_B = \frac{(1.362~A)^2~(5.50~H)}{2}$
$U_B = 5.10~J$
The energy stored in the magnetic field is $~~5.10~J$
