Chapter 23, Problem 23.9DQ

If you carry out the integral of the electric field ${\displaystyle \int \stackrel{\to }{\text{E}}}\cdot \stackrel{\to }{\text{dl}}$ for a closed path like that shown in Fig. Q23.9, the integral will always be equal to zero, independent of the shape of the path and independent of where charges may be located relative to the path. Explain why.

Figure Q23.9