Verify if the following vector fields are conservative: a) A₁ (+-) 1 = b) ₂ = (xy, yz, zx) c) A3 = (x-xeª, -y, e²) In case they are conservative, find their respective potential fields.

Suppose that the electric potential ? in a certain region is given by V=Ax2−Bx+C where A=2.15 V/m2, B=3.65 V/m, and C=7.55 V. Find the magnitude of the electric field E at the point ?=1.35 m. E=?

Find the electrostatic potential difference between points B and C (V(B)-V(C)=?) region that is being generated due to the Q=-3 C load homogeneously distributed on the insulating shell with radius R=a and Q = +4 C load homogeneously distributed on the insulating shell with radius R=b given in the figure. C(3,3,3) Z B(2,2,2) ● b. ►Y