The electric field in a region of space has the components ey = ez = 0 and ex = (4.00 n/c · m) x. point a is on the y axis at y = 3.80 m, and point b is on the x axis at x = 4.40 m. what is the potential difference vb − va?

Explanation:

Consider the axis diagram attached.

Given:

                                        Ey = Ez = 0

                                       Eₓ = - 4x N/C · m

Since electric field is in x direction, potential difference would be:

Here we integrate between limits 0 and 4.40 which is distance between A and B along x-axis.  

see the picture for the vector

the magnitude of the vector by pythagorean theorem

r = √( (-10)^2 + (3)^2 ) = √109

magnitude = √109 units

the direction angle between vector and x-axis is

tan^(-1)(3/10) = 16.699

so the direction is approximately 16.7 degrees north of west