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.

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CataleahC155300 CataleahC155300 · Answer 1 · 2022-10-26T01:28:36+02:00

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

[tex]U=\frac{kQ}{r}[/tex]

For the charge of 3.08 μC

[tex]U_{3.08}=\frac{(8.988\times10^9)(3.08\times10^{-6})}{(0.41)}=67476.27V[/tex]

For the charge of -15.82 μ C:

[tex]U_{-15.82}=\frac{(8.988\times10^9)(-15.82\times10^{-6})}{(0.41)}=-346805.27V[/tex]

For the charge of -3.61 μC:

[tex]U_{-3.61}=\frac{(8.988\times10^9)(-3.61\times10^{-6})}{(0.41)}=-79138.24V[/tex]

And for the charge of 9.7 μC:

[tex]U_{9.7}=\frac{(8.988\times10^9)(9.7\times10^{-6})}{(0.41)}=212642.93V[/tex]

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

[tex]\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}[/tex]

Answer:

-145824.31 V