Calculate \(E_{x}\) for each potential:

(a) \(V(x)=a+b x\), \(a=4000 \mathrm{~V}, b=6000 \mathrm{~V} / \mathrm{m}\).

(b) \(V(x)=a x+b / x\), \(a=1500 \mathrm{~V} / \mathrm{m}, b=2000 \mathrm{~V} \cdot \mathrm{m}\).

(c) \(V(x)=a x-b x^{2}\), \(a=2000 \mathrm{~V} / \mathrm{m}, b=3000 \mathrm{~V} / \mathrm{m}^{2}\).

(d) \(V(x)=-2000 \mathrm{~V}\) (independent of \(x\) ).