Three nonconducting infinite sheets are parallel to the \(y z\) plane of an \(x y z\) coordinate system. Each sheet has a uniform surface charge density. Sheet 1 , negatively charged with surface charge density \(-\sigma\), passes through the \(x\) axis at \(x=1.0 \mathrm{~m}\). Sheet 2 has an unknown surface charge density and passes through the \(x\) axis at \(x=2.0 \mathrm{~m}\). Sheet 3 , negatively charged with surface charge density \(-3 \sigma\), passes through the \(x\) axis at \(x=4.0 \mathrm{~m}\). The electric field due to the sheets is zero at \(x=1.5 \mathrm{~m}\).

(a) What is the surface charge density on sheet 2? If the electric field at \(x=0\) is \(\vec{E}_{0}\), what is the electric field at

(b) x=-2.0 m,

(c) x=3.0 m, and 

(d) x=6.0 m ?