To determine the dimensions of the quantity $Li^2$, we can relate it to the energy stored in an inductor.

1. Formula: The work done ($W$) required to build up a current $I$ in an inductor of inductance $L$ is stored as magnetic potential energy. The expression is given by $W = \frac{1}{2}LI^2$ .
2. Dimensional Analysis: Since the factor $\frac{1}{2}$ is a dimensionless constant, the dimensions of $Li^2$ are identical to the dimensions of Work or Energy.
3. Dimensions of Energy: The dimensional formula for Work/Energy is $[ML^2T^{-2}]$ .
4. Verification: Inductance ($L$): Dimensions are $[ML^2T^{-2}A^{-2}]$ . Current ($i$): Dimensions are $[A]$.

• $Li^2 = [ML^2T^{-2}A^{-2}] \times [A]^2 = [ML^2T^{-2}]$.

Therefore, the dimensions of $Li^2$ are $[ML^2T^{-2}]$.