Find the dimensions of capacity ($X$): Capacitance $C = \frac{Q}{V} = \frac{Q^2}{W}$. Since $Q = [AT]$ and Work $W = [ML^2T^{-2}]$, $[X] = \frac{[AT]^2}{[ML^2T^{-2}]} = [M^{-1} L^{-2} T^4 A^2]$.

Find the dimensions of magnetic field ($Z$): Magnetic force $F = qvB \implies B = \frac{F}{qv}$. Since $F = [MLT^{-2}]$, $q = [AT]$, and $v = [LT^{-1}]$, $[Z] = \frac{[MLT^{-2}]}{[AT][LT^{-1}]} = [M T^{-2} A^{-1}]$.

Calculate the dimensions of $Y$: Given $X = 3YZ^2 \implies Y = \frac{X}{3Z^2}$. Ignoring the dimensionless constant $3$, we get: $[Y] = \frac{[X]}{[Z]^2} = \frac{[M^{-1} L^{-2} T^4 A^2]}{[M T^{-2} A^{-1}]^2}$ $[Y] = \frac{[M^{-1} L^{-2} T^4 A^2]}{[M^2 T^{-4} A^{-2}]} = [M^{-3} L^{-2} T^8 A^4]$.