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# Three equal positive charges are at the corners of an equilateral tri- angle of side a as in Figure P15.38. Assume the three charges together create an electric field. (a) Sketch the electric field lines in the plane of the charges. (b) Find the location of one point (other than `) where the electric field is zero. What are (c) the magnitude and (d) the direction of the electric field at P due to the two charges at the base?

## Therefore, the direction at point $\mathrm{P}$ due to the two charges is $[\text { upward }]$

### Discussion

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##### Christina K.

Rutgers, The State University of New Jersey

##### Andy C.

University of Michigan - Ann Arbor

##### Aspen F.

University of Sheffield

### Video Transcript

have to bury slur, start our discussion. Suppose you have a triangle. And on each corner off strangled. There's a positive charge, Q Okay. No, you have to draw the electric field bedroom for this charge system. Okay, so basically, these all have three positive charges. Similar charges always repel so electric. Feel like that? Some. These are the back turn off electrical lines for a triangle system. Basically, these are the adults. Ah, that shows that direction off electric field. That is from positive to what's negative. Now suppose you have to find a point in which the neck electric fold Phyllis issue. OK, but the condition is that you can't choose infinity. Okay? Support if this is the three charges system the only point at which the electric field is Jiro. Because the these three charges are off similar magnitude. The point lies on the central because let if I had named the corner string wanted the electric field by of one lies in this direction. Even an electric field by two allies in destruction 82 and electric food by three lies in destruction. So the net result and electric field off a to an e three realizing this direction, and this 8 to 3 is exactly cancel a by the heat. Even so, basically, the next electric field at the center will be chill. So Santa is the only point other than infinitely bayonet like to feel this. Jiro No suppose in the similar triangle their charges are Q Q Q thistles. The point B. Okay, now you have to find out the Net electric field on this point. B Do you grow these point on? There's named in Q and this art. Okay, so electric field at B due toa que will be one up on four by up silent note que by a square If the side of over triangle is a meter Okay, you don't book will And this electric really is lies realise in each direction e que Okay. Similarly, electric will don't be due to our will be one upon four by upside and north you buy a square new timber column. But this electric sale realizing this direction No, the night electric field at point B will be you net and this lies in destruction. See, this is the collector triangle because all types are saying so, angle between them is 60 degree hold angles are See if this angle is 60 degree by vertical deposit angle. This angle will also 60 lately. Now we have to find out the net result An electric field between Ikuo and Ear and also ah e p r and d pick you and also the magnitude off e p r. Is it close to magnitude off A b que Let's name say it is 1/4 e. Okay, so So we know the form, love, result and electric. So we know the formula off certain electric field that is even square. Plus a two square plus two, even you to course eater. And for in this case, cheetahs ecstatically So course sixties one by two. So this two will cancel out by Costa. Okay, so and even if you is equivalent to eat so we will get you square plus e square less east square. So it will be groupie e and it would be rude. Three in tow one upon four by absolute North. Que by a square Newton Bach. Coolum. So this is the net electric Feel at point. Be Okay. Well, this is all from me for this video. I hope you will like the video. Thank you.

Other Schools
##### Christina K.

Rutgers, The State University of New Jersey

##### Andy C.

University of Michigan - Ann Arbor

##### Aspen F.

University of Sheffield