Question

The electric field $\overrightarrow{E}$ in the overlapped region is

• A. non-uniform
• B. zero
• C. $\frac{p}{3{\epsilon }_0}\overrightarrow{d}$
• D. $\frac{-p}{3{\epsilon }_0}\overrightarrow{d}$

Answer 1

The correct option is C $\frac{p}{3{\epsilon }_0}\overrightarrow{d}$

Take a point P in overlap region, then for triangle $O_1{O}_{2}P$ $\overrightarrow{r_1}-\overrightarrow{r_2}=\overrightarrow{d}$

${\overrightarrow{E}}_P=\frac{p\overrightarrow{r_1}}{3{\epsilon }_0}-\frac{p\overrightarrow{r_2}}{3{\epsilon }_0}$

$=\frac{p}{3{\epsilon }_0}({\overrightarrow{r}}_1-{\overrightarrow{r}}_2)=\frac{p\overrightarrow{d}}{3{\epsilon }_0}$

This is the uniform field in overlap region.