Answer to Question #124315 in Classical Mechanics for bob

Question

Four protons form a square of side length a . what is the electric potential in the center of the square ?

Answer 1

Let us denote the charge on a proton is $p=1.602\times 10^{-19}C$

Now, each sides of the square is $a$ ,thus distance between each corner from the center of the square will be

$$\frac{a}{\sqrt{2}}$$

Potential due to each charge is

$$V_i=\frac{1}{4\pi\epsilon_0}\frac{p}{\frac{a}{\sqrt{2}}}=\frac{1}{4\pi\epsilon_0}\frac{\sqrt{2}p}{a}$$

Thus, potential at center of the square is

$$\sum_{i=1}^{4}V_i=\frac{\sqrt{2}}{\pi\epsilon_0}\frac{p}{a}$$