In: Physics

# What is the electric potential at the point indicated with the dot in (Figure 1)?

What is the electric potential at the point indicated with the dot in (Figure 1)?

figure 1

## Solutions

##### Expert Solution

Potential at given point due to point charge $$=\mathrm{kQ} / \mathrm{r}$$

Potential at a point due to multiple point charges $$=\mathrm{kQ}_{1} / \mathrm{r}_{1}+\mathrm{kQ}_{2} / \mathrm{r}_{2}+\mathrm{kQ}_{3} / \mathrm{r}_{3} \ldots \ldots$$.etc

From the figure

$$V=k Q / r_{1}+k Q / r_{2}+k Q / r_{3}$$ as all the charges are equal

$$V=k Q\left(1 / r_{1}+1 / r_{2}+1 / r_{3}\right)$$

$$r_{1}=3 \mathrm{~cm}=0.03 \mathrm{~m}$$

$$r_{3}=4 \mathrm{~cm}=0.04 \mathrm{~m}$$

$$r_{2}=\sqrt{\left(r_{1}^{2}+r_{3}^{2}\right)}$$

$$\Rightarrow r_{2}=\sqrt{\left(0.03^{2}+0.04^{2}\right)}$$

$$\Rightarrow r_{2}=\sqrt{(0.0025)}$$

$$r_{2}=0.05 \mathrm{~m}$$

$$Q=2 n C=2^{*} 10^{-9} C$$

$$\mathrm{k}=9^{*} 10^{9} \mathrm{Nm}^{2} / \mathrm{C}^{2}$$

$$V=9 * 10^{9} * 2 * 10^{-9}(1 / 0.03+1 / 0.05+1 / 0.04) V$$

$$\Rightarrow V=18 * 78.33 V$$

$$\therefore V=1410 \mathrm{~V},$$ which is the required solution