In a rectangular coordinate system, a positively charged infinite sheet on which the surface charge density is \(+2.5 \mu \mathrm{C} / \mathrm{m}^{2}\) lies in the \(y z\) plane that intersects the \(x\) axis at \(x=0.10 \mathrm{~m}\). What are

(a) \(\vec{E}\) for \(x>0.10 \mathrm{~m}\) and

(b) the potential difference \(V(0.20 \mathrm{~m})-V(0.50 \mathrm{~m})\) ?

(c) A \(+1.5-\mathrm{nC}\) charged particle is initially at \(x=0.50 \mathrm{~m}\). How much work must an external agent do to move this particle to \(x=0.20 \mathrm{~m}\) ?

\((d)\) Taking the potential to be zero at the sheet, draw three equipotential surfaces at \(20-\mathrm{V}\) intervals on each side of the plane, labeling each surface with its potential value.