A uniform field of magnitude E = 2000 N/C is directed $\mathrm{\theta }={37}^{\circ }$ below the horizontal. Find the potential difference between P and R $\left({\mathrm{V}}_{\mathrm{P}}-{\mathrm{V}}_{\mathrm{R}}\right)$ (in volts).

The potential difference between two points P and R in electric field is, ${\mathrm{V}}_{\mathrm{P}}-{\mathrm{V}}_{\mathrm{R}}=-{\int }_{\mathrm{R}}^{\mathrm{P}} \overrightarrow{\mathrm{E}}\cdot \overrightarrow{\mathrm{dl}}$

As electric field is constant, 

${\mathrm{V}}_{\mathrm{P}}-{\mathrm{V}}_{\mathrm{R}}=-{\int }_{\mathrm{R}}^{\mathrm{P}} \overrightarrow{\mathrm{E}}\cdot \overrightarrow{\mathrm{dl}}$

${\mathrm{V}}_{\mathrm{P}}-{\mathrm{V}}_{\mathrm{R}}=-\overrightarrow{\mathrm{E}}\cdot {\int }_{\mathrm{R}}^{\mathrm{P}} \overrightarrow{\mathrm{dl}}=-\overrightarrow{\mathrm{E}}\cdot \left(\overrightarrow{{\mathrm{r}}_{\mathrm{P}}}-\overrightarrow{{\mathrm{r}}_{\mathrm{R}}}\right)$

$\Rightarrow {\mathrm{V}}_{\mathrm{P}}-{\mathrm{V}}_{\mathrm{R}}=-\overrightarrow{\mathrm{E}}\cdot \mathrm{\Delta }\overrightarrow{\mathrm{l}}=-\mathrm{E}\cdot \mathrm{\Delta l}\cdot \cos \left({180}^{\circ }-\mathrm{\theta }\right)$

Here, $\mathrm{\Delta l}=\mathrm{PR}=5 \mathrm{cm}=5\times {10}^{-2} \mathrm{m}$

Hence, ${\mathrm{V}}_{\mathrm{P}}-{\mathrm{V}}_{\mathrm{R}}=-2000\times 5\times {10}^{-2}\left(-\cos {37}^0\right)$

$=2000\times 5\times {10}^{-2}\times \frac{4}{5}=80 \mathrm{V}$