Question

Calculate the electric potential energy of the arrangement described as follows: Four charges are placed at the corners of a 29.01 cm square. The particles are as follows: 3.08 microC at x =0, y = 0, -15.82 microC at x = 29.01, y = 0, -3.61 microC at x = 29.01, y = 29.01, and 9.7 microC at x=0 and y = 29.01.

Answer 1

We can calculate the electric potential energy of each individual charge using the following formula:

`U=(kQ)/(r)`

For the charge of 3.08 μC

`U_(3.08)=((8.988*10^9)(3.08*10^(-6)))/((0.41))=67476.27V`

For the charge of -15.82 μ C:

`U_(-15.82)=((8.988*10^9)(-15.82*10^(-6)))/((0.41))=-346805.27V`

For the charge of -3.61 μC:

`U_(-3.61)=((8.988*10^9)(-3.61*10^(-6)))/((0.41))=-79138.24V`

And for the charge of 9.7 μC:

`U_(9.7)=((8.988*10^9)(9.7*10^(-6)))/((0.41))=212642.93V`

Therefore, the electric potential at the center due to the the four charges is:

`\begin{gathered} U=U_(3.08)+U_(-15.82)+U_(-3.61)+U_(9.7) \\ U=67476.27-346805.27-79138.24+212642.93 \\ U=-145824.31V \end{gathered}`

Answer:

-145824.31 V