Question

Calculate the electric potential energy on the center of the square of the arrangement described as follows: Four charges are placed at the corners of a 11.36 cm square. The particles are as follows: 10.46 microC at x =0, y = 0, -11.34 microC at x = 11.36, y = 0, -16.6 microC at x = 11.36, y = 11.36, and 14.95 microC at x=0 and y = 11.36.

Answer 1

Our arrange looks like the following:

The potential energy in each individual point is given by:

`E_p=k(Q)/(d)`

As all points have the same distance from the center of the square, we can calculate a single distance. We'll need the pythagorean theorem in order to calculate the distance. It can be written as the following

`c^2=a^2+b^2`

Then we can calculate this using half the side of the square. We get

`c^2=5.68^2+5.68^2`

By isolating c we can find

`c=\sqrt[2]{5.68^2+5.68^2}=8.03cm`

This is the distance from each vertex to the center

We also need to take into account the fact that the total potential energy is the sum of potential energies

`E_p=E_A+E_B+E_C+E_D`

It can then be written as

`E_p=k((q_1)/(d)+(q_2)/(d)+(q_3)/(d)+(q_4)/(d))`

Which, once we plug our values in, yields:

`E=(9*10^9)(((10.46-11.34-16.6+14.95)*10^(-6))/(8.03*10^(-2)))=-283561.6438J`

Thus, our final answer is 283561.6438J