A particle carrying \(3.00 \mathrm{nC}\) of positive charge is at the origin of a rectangular coordinate system, and a particle carrying \(3.00 \mathrm{nC}\) of negative charge is on the \(x\) axis at \(x=6.00 \mathrm{~m}\).

(a) Calculate the potential on the \(x\) axis at \(x=3.00 \mathrm{~m}\), relative to zero potential at infinity.

(b) Calculate the electric field on the \(x\) axis at \(x=3.00 \mathrm{~m}\).

(c) Calculate the potential on the \(x\) axis at \(x=3.01 \mathrm{~m}\).

(d) Compute \(\Delta V / \Delta x\) for \(\Delta V\) between \(x=3.00 \mathrm{~m}\) and \(x=3.01 \mathrm{~m}\), and \(\Delta x=0.01 \mathrm{~m}\), and compare your result with your result in part \(b\).