Physics - Electrostatics Question with Solution | TestHub

Superpose: a full xy-plane of density $-\sigma$ gives $E_z=-\frac{\sigma }{2{\epsilon }_0}$ on the whole +z axis; the first quadrant carries an extra $+2\sigma$, and an infinite quarter-plane contributes $E_z=\frac{2\sigma }{8{\epsilon }_0}=\frac{\sigma }{4{\epsilon }_0}$, uniform along z.

Net: $E_z=-\frac{\sigma }{4{\epsilon }_0}$.

Work done by the field from $(0,0,d)$ to $(0,0,2d)$: $W=q{E}_{z}d=-\frac{\sigma qd}{4{\epsilon }_0}$ - (A)