Question #42764

A large tank contains a liquid of uniform density $\rho$. The tank accelerates horizontally to the right ($+\hat{i}$ direction) with a constant acceleration $a = g$. A rigid, thin-walled, uncharged conducting spherical shell of outer radius $R$ is completely submerged in the liquid and held fixed relative to the tank. The cavity inside the shell contains a gas of negligible mass. A point charge $+Q$ is held fixed at the exact center of the cavity. A uniform external electric field $\vec{E}_0 = E_0 \hat{i}$ is applied horizontally to the right. Let $\vec{F}_e$ be the net electrostatic force exerted on the point charge $+Q$. Let $\Delta P_{out} = P_{out, L} - P_{out, R}$ be the difference in mechanical pressure between the leftmost point ($P_{out, L}$) and the rightmost point ($P_{out, R}$) on the outer surface of the shell. Let $\Delta P_{in} = P_{in, L} - P_{in, R}$ be the difference in gas pressure between the leftmost point ($P_{in, L}$) and the rightmost point ($P_{in, R}$) on the inner surface of the shell. Which of the following sets of values is correct?