Four charges, each of value q, are placed at the four corners of a square of side a. What is the potential at the centre of the square

Four charges, each of value q, are placed at the four corners of a squ

1.	Four charges, each of value q, are placed at the four corners of a square of side a. What is the potential at the centre of the square
Answer» <html><body><p></p>Solution : Consider four masses each of <a href="https://interviewquestions.tuteehub.com/tag/mass-1088425" style="font-weight:bold;" target="_blank" title="Click to know more about MASS">MASS</a> m at the corners of a square of side l,We have four mass pairs at <a href="https://interviewquestions.tuteehub.com/tag/distance-116" style="font-weight:bold;" target="_blank" title="Click to know more about DISTANCE">DISTANCE</a> l and two diagonal pairs at distance`sqrt(<a href="https://interviewquestions.tuteehub.com/tag/2-283658" style="font-weight:bold;" target="_blank" title="Click to know more about 2">2</a>)`l <br/> hence, <br/> W(<a href="https://interviewquestions.tuteehub.com/tag/r-611811" style="font-weight:bold;" target="_blank" title="Click to know more about R">R</a>)= - <a href="https://interviewquestions.tuteehub.com/tag/4-311707" style="font-weight:bold;" target="_blank" title="Click to know more about 4">4</a> `(Gm^(2))/(l) - 2 (Gm^(2))/(sqrt(2)l)` <br/>= - `(2.Gm^(2))/(l ) (2 + (1)/(sqrt(2))) = - 5.41 (Gm^(2))/(l)`<br/> The gravtational potential at the centre of the square `(r = sqrt(2)l//2)` is<br/> U(r)= - `4 sqrt(2) (Gm)/(l)` . <br/> <img src="https://doubtnut-static.s.llnwi.net/static/physics_images/NCERT_TAM_PHY_XI_P1_C08_SLV_003_S01.png" width="80%"/></body></html>