Question #42786

A parallel plate capacitor consists of two rectangular plates of length $L$ and width $w$, separated by a distance $d = 4.00 \text{ mm}$. A dielectric slab of length $L$, width $w$, thickness $t = 2.00 \text{ mm}$, and dielectric constant $k = 2$ is partially inserted a distance $x$ between the plates, parallel to the plates. A constant potential difference $V$ is maintained across the capacitor. The electric force $F$ pulling the slab into the capacitor is calculated from the system's parameters. If the maximum absolute errors in measuring the slab thickness and plate separation are $\Delta t = 0.03 \text{ mm}$ and $\Delta d = 0.024 \text{ mm}$ respectively, what is the maximum percentage error in the calculated value of $F$? (Assume $V$, $L$, $w$, and $k$ are exact constants, and edge effects are negligible).