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# Four point charges are at the corners of a square of side $a$ as shown in Figure P15.8. Determinethe magnitude and direction of the resultant electric force on $q$ with $k_{c}, q,$ and a left in symbolicform.

## See work for solution.

### Discussion

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##### Top Physics 102 Electricity and Magnetism Educators ##### Andy C.

University of Michigan - Ann Arbor

LB ##### Aspen F.

University of Sheffield ##### Jared E.

University of Winnipeg

### Video Transcript

How strings. Let's start our discussion. Electrostatic force. Okay, Now suppose you have a square. Okay? I'm giving the corner numbers off this square. Born toe 34 Suppose on these corners in the corner were in charge. Who is placed in corner to charge? Tokyo is placed in corner three. Charged three Q is place and in corner four charge took us place. These are the corner numbers. Okay, Now we have to find out the exact force that is exerted by these charges. Tokyo trick you and took you on this charge. Q. Okay, So the force on one do toe do that is force on one. Do toe to is in this direction F one. Okay. And it will be okay. You want cute? Oh, by the square and a job. The square is a centimeter. Okay. Hey, Square. So what's the value off ruining? You do a que in tow? Took cube and toe. Took you by s with K F 12 Okay, I am taking only the magnitude here. So it will comes toe may toe ok, que square by a square F one Newton. Ok, and I'm showing their direction here. This isn't this direction. Okay, Now the force on one due to four. This will be in this direction. Four for one due to four. Okay, then it will be okay. Q one Q four by a square. The value off Q one is Q and Q Forest took you then It is similar to have one too, and it will comes to obey. Okay, Cue square by a square, you don't No. See, these f one and F 14 are at 90 degree. OK, but let the angle between them is 90 degree. So now we have to find out the result in force between them. Suppose I name the result and force off fund for and F one toe, half dish. Okay, so we know the formula of a certain forces are f result and will be Underwood Afrin square plus after square plus toe are fun after course data. Now the angle between them is 90 degree. Okay, So value. Of course, 19 0 So it will comes at fun square place after square. But for this case, it is af 12 square plus f one force quell. This time will be geo due to course 90 and half resultant his after show. Okay, now, if you put the values basically the magnitude off F one and F 1 40 similar So it will comes to be to have fun to square and it will comes. Toby's your toe. Do kick you square by a square. This is the venue off after sh seeing this in the square? No. We resort the forces due to one and four in after sh with half dish birthday. The force is also exerted on one due to three. That is F one thing. The value of F 13 magnitude is okay, Q one Q t by a root two square Because the Dagnall off the square is off site a route OK from here it will comes to be own tart. The charge trick you is life. Okay, so it will comes to be free Kick you square by two s quit. No, we have to find out the next result and force on this charge one. Now, after between abduction after country, the angle between after dash and F one tree is Jiro is chill so of by the result and formula. You see in the figure If I will put this the value of course. Tutor here, Jiro. Then it will comes to the Afghan square. First have to square place to have fun to have toe So happy days Because to Jiro it will comes Toby after because toe have fun. Plus after basically the whole square form level generate it weakens Lord with the route So Afghan plus after will it comes off. It means that half resultant or half net will be We have to just simply add them Toa que square by square plus three by toe Kick you square by square. This will be Toto plus three by two Kick you square by a square. Hence, this is the net result and force on child or not, It is the only magnitude on charge. Cool. And its direction his decide. This is the natural Surgeon Force. Okay, basically, I'm making us. They're easy. This will be the net resultant force in charge one in this direction. Okay. And this is the magnitude. Well, this is all for me for this video. I hope you will like the video. Thank you. Other Schools
##### Top Physics 102 Electricity and Magnetism Educators ##### Andy C.

University of Michigan - Ann Arbor

LB ##### Aspen F.

University of Sheffield ##### Jared E.

University of Winnipeg