C

Step 1: The formula for the energy stored in an inductor is given by:
$$ U = \frac{1}{2} L i^2 $$
where $$ U $$ is energy, $$ L $$ is self-inductance, and $$ i $$ is the current.
Step 2: The unit of energy (U) is Joules (J), the unit of current (i) is Amperes (A), and we need to solve for the unit of inductance (L).
Step 3: Rearranging the formula for inductance gives:
$$ L = \frac{2U}{i^2} $$
Step 4: The unit of inductance can be derived as follows:
- Energy in Joules: J = kg·m²/s²
- Current in Amperes: A
Therefore, the unit of inductance is:
$$ L = \frac{2\, (kg\cdot m^2/s^2)}{A^2} $$
Step 5: The derived unit can also be expressed as:
$$ L = \frac{kg\cdot m^2}{A^2\cdot s^2} $$
Step 6: This matches the unit of Henry (H), the SI unit of inductance, which is derived as: H = $$ \frac{kg\cdot m^2}{A^2\cdot s^2} $$
Therefore, the correct answer is C: Henry (H).