A positively charged infinite sheet has a surface charge density of \(+5.0 \mathrm{nC} / \mathrm{m}^{2}\). What is 

(a) the electric field at a distance \(0.10 \mathrm{~m}\) from the sheet and 

(b) the potential difference between two points located at distances of \(0.30 \mathrm{~m}\) and \(0.50 \mathrm{~m}\) from the sheet?

(c) \(\mathrm{A}+3.0 \mathrm{nC}\) charged particle is initially at a distance \(0.50 \mathrm{~m}\) from the sheet. How much work must an external force do to move this particle to a distance of \(0.30 \mathrm{~m}\) from the sheet?

(d) Taking the potential to be zero at the sheet, at what distances from the sheet are the equipotential surfaces having potential of magnitudes \(20 \mathrm{~V}, 40 \mathrm{~V}\), and \(60 \mathrm{~V}\) ?