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# Three point charges are located on a circular arc as shown in Figure $\mathrm{P} 15.30 .(\mathrm{a})$ What is the total electric field at $P,$ the center of the arc? (b) Find the electric force that would becxerted on a $-5.00$ -nC chargc placed at $P .$

## a. $1.80 \times 10^{3} \mathrm{N} / \mathrm{C}$b. $9.00 \times 10^{-5} \mathrm{N}$

### Discussion

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##### Christina K.

Rutgers, The State University of New Jersey

LB
##### Marshall S.

University of Washington

### Video Transcript

hair strands. Let's start our discussion. Suppose three point charges are looking on an act. This is a circular arc. And at this point, a charge off three no cual a misplaced. And at this point, charge off, minus student and Aquila misplaced. And at this point, charge off. Three Nakoula miss placed. Okay, No, at point B, we have to find out the net electric field. So basically, this is the line joining the point and angle from where a gentler 30 degree Okay. And the stands between this point to this point is four centimeter. So basically, this is a circle act, so all line joining the point are four centimeter. Okay, let's name the corners. Fun, too. Three No electric field on be due to one will be Que que won by our square. And that will be nine into 10. This by nine in tow. Three in tow. Tennis part might. Minus fear is par minus nine. Willem by June 1. Judo Fort meter square. Okay, now, by solving this, you will get the value. 1675 new temple cooler. The magnitude off e p one is similar to magnitude off. Hey, Petri. Because all conditions are same value off the magnitude of charge and understand. Okay, So basically a P three that is electric Phelan p due to chance three and he'd be one The electrical field on page of the charge one is in this direction. Know the result in between them? Let me. The 13 is the result between them. Okay, We know love from love. Resulting electric field that is Thunder road, even square bless you to square. Let's to even a to goes Tita. Okay, so no, here are BP one square, plus he be three square closed toe e b u one e victory goes 60 because here the total anger is 60 So from vertical oppose it angle these and this angle is also 16 agree And the value of course, extra degrees one by toe So we will get And the magnitude off even is similar to a Petri. So it will be e p one square plus e p one square plus e p one square because course sixties two into one by two value of course 60 and keep even an e p true easy out of equal manager. So from here PP on square comes so it will be Route three. Eveyone leave won t route Creepy one and that will be route tree in tow. 16875 New Temple, Coolum and we will get 49 to 8.3 in new temper. Coolum Electric Field. But there's also a charge on position Tomb So electric field at B due to position too is e B two. Get you to buy our square and that will be nine into tennis by nine in tow. Two into 10 This par minus nine by Cheeto Point Cheeto four meter square. So by solving this, we will get the answer. 11 250 Newton or Coolum. Now, in this condition, E b. He won three is in this direction and e p two is in this direction. So we have to find out the net result in field on B So basically this is they are at the Anglo 1 80 degree so value, of course, 1 80 degree is minus. One sober result and value will be unit will be it 13 minus e B two, because it originated the whole square formula and the route will be cancel. Oh, okay. So we're simply we can simply minus them. So through nine to do a woman clean minus 11250 A new temper. Coolum. By subtracting this 179 78 20 Newton Bach. Coolum is the value is the magnitude all net electric field. And this electric feel is in this direction means this is the point B. So net electric field isn't this direction even that. Okay, now let us suppose at point B a charge of five men Coolum is published, so we have to find out the net electrostatic force on this point. Okay, this is Oversupply Rock. So basically, that electric field is this. So next electrostatic force will be que e a truly be five into 10 minutes. Par minus nine in tow. 17978 20 Newton. We will get our final force 8.98 in tow. 10 less by minus five in Newton. This is a net electrostatic force at point. Big if would placed a charge off five Nano Ola Minus final Coolum at the position. 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

LB
##### Marshall S.

University of Washington