Question

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?

Answer 1

Answer:

   $V_{b}-V_{a} = -38.72$

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:

              $V_{b} - V_{a} =-\int\limits^{4.40}_{0} {E_{x} } \, dx$

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

              $V_{b} - V_{a} = -4 \left[\begin{array}{ccc}\frac{x^{2} }{2} \end{array}\right]^{4.40}_{0}$

                       $V_{b}-V_{a} = -4 (9.68)\\V_{b}-V_{a} = -38.72$