Physics - Electrostatics Question with Solution | TestHub

Superpose a full layer of density $\rho$ with a sphere of density $-\rho$.

(A) At A (mid-plane of the layer, on the cavity surface): the layer's field is zero; the sphere contributes $\frac{\rho (h/2)}{3{\epsilon }_0}=\frac{\rho h}{6{\epsilon }_0}$ toward right - (A)

(B) At B (above the layer): $\frac{\rho h}{2{\epsilon }_0}-\frac{\rho h}{6{\epsilon }_0}=\frac{\rho h}{3{\epsilon }_0}$ upward - (B)

(C), (D): direct computation gives $V_A-V_C=-\frac{\rho h^2}{24{\epsilon }_0}$ and $V_B$ differing from the printed values - wrong.