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Problem 16 Medium Difficulty

Particle $A$ of charge $3.00 \times 10^{-4} \mathrm{C}$ is at the origin, particle $B$ of charge $-6.00 \times 10^{-4} \mathrm{C}$ is at $(4.00 \mathrm{m}, 0),$ and particle $C$ of charge $1.00 \times 10^{-4} \mathrm{C}$ is at $(0,3.00 \mathrm{m})$ , (a) What is the $x$ -component of the electric force exerted by $A$ on $C$ ? (b) What is the y-component of the force exerted by $A$ on $C^{2}(c)$ Find the magnitude of the force exerted by $B$ on $C .$ (d) Calculate the $x$ -component of the force exerted by $B$ on C. (e) Calculate the $y$ -component of the force exerted by $B$ on $C$ (f) Sum the two $x$ -componcnts to obtain the resultant $x$ -component of the electric force acting on $C$ (g) Repeat
part (f) for the $y$ -component. (h) Find the magnitude and direction of the resultant electric force acting on $C .$

Answer

A. 0.0 $\mathrm{N}$
B. 30.0 $\mathrm{N}$
C. 21.6 $\mathrm{N}$
D. 17.3$N$
E. $-13.0 N$
F. 17.3 $\mathrm{N}$
G. 17.0$N$
H. $24.3 N, 44.5^{\circ}$

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Video Transcript

harassed ranks. Let's start our discussion on electrostatic force. Suppose we have a co ordinate system in which a point a lie that origin and at a a charge off tree in tow. 10 days by minus four Fulham charges place at point B four Coma Jiro meter charge off minus six in pretenders Bar minus four. Cola misplaced. And at one See, that is Cheeto Coma Tree A charge off one into tangles by minus four. Coolum is placed. Okay? No, like a sea like this. Flying forces on Brady's condition. No flush. Firstly, what is the X component off force that is exerted on sea by it means we have to find are the X component off. Fourth on, See, due to a basically, forcing due to a is purely invite direction that is in a poor direction. So x component off. This is Joe that is at sea access Jiro. Okay, now we have to find out of I component of force on seed you may have seen right. That is K Q one duty by our country square, That is Ah, nine into tenders by nine into three in tow. Attendance by minus four into one into 10. This part minus four by three meters squared. OK, if you solve this core values, you will get the answer off. 30 Newton. This is in positive y direction that isn't off for direction. Okay, this is the direction off FC and positive I traction. Okay, Now you have to find out the force on C Do Do be. No leg was supposed a the triangle condition. Ah, this is three meter and this is four meter no charge off minus six. Inter tenderness. Par minus four. Cola misplaced. Here. And chart one intact, endless par minus four will have is placed here. This is buoyancy and disappointment. Now, this baby exert force on seat to watch yourself. Okay. So forth on C due to be will be okay, Butto beauty by our B C square Or you considered are two or three square if this is the 0.3 and this is the point to so our duty square. Okay, uh, basically the value of our 23 this fight. If you see, this will be a right angle triangle. This is four meter and this is three meter. So from high Pythagoras tour, um, this will come. So, Toby, five meter. So if I put the values nine into tennis by nine into a six Inter tenders by minus. For in the values here, we are taking only magnet yours. Okay, Uh, one entertain this part minus four by five square. If you solve this, you will get the value of 21.6 21 0.6 Nuta. This is force on C exerted by B O only magnitude. Okay, Now you have to find out the X component off this foot. Basically, this force exerted in this direction because this is negative charge and this is positive charge, it will attract waters. And the X component is in this direction. That is absolutely X. And the vie component is in this direction. That is FCB. Why so teachable comes here? Because this is the extraction. The X component off this force FCB will be fcv course cheetah. Okay, The value off fcv is 21.6 Newton and the value of course to ties based upon hyper two news, that is oh, high protein is's or five and bases off foot. That is four. By fight into four by five, you will get the X component off. This force is 17 point toe it Newton for Vikram. Moment off. This force is FCB scientist. This is why complaining 21.6 in tow. Scientist. It will be three by four that is prophetically born High party Gnaeus two by four you will get the value 12.96 Newton. But this force exerted negative Y direction that is in a downward direction. So the negative science will comes off. Okay, this is the now let us suppose we have to find out the net result and force won't see that is exerted by both A and B but only in X company. Basically force on sea do toe X component of forcing c x component off fourth seed You okay plus X component or force on C due to be basically, this will be Jiro because they're no forced life and test will be. We find out earlier 17.28 Newtons. So net force on axe direction means next four Xanax. Campell names will be 17 going the mutant. Okay, Now we have to find out the vie component off, resulting force this on C do end. Basically vie component off force on C will be by component for foursome CDO a plus bi component off fours. Uh, on seeing you to be okay, so we find out that I see is 30 Newton in a poor direction. Plus, basically, this is in the negative by a negative y direction. Then it will be minus off 12.96 newton. Then it will comes to me. 17.4 Neutra in ah, four direction. This is the vie component off net result in force on C. Okay. Thank you. Now you have to find other net force on sea. Do A and B. Okay, so, uh, if I assume, like like a triangle, then this is 44 seed. You do a A. This is force on seed you to be and the net result enforce. Will, comes off somewhere like here. Some. They're like absi dessert. Okay. Not to solve this, we have to find out first the angle between them Basically, if I make a line here and this is will be 90 degree love, we have to find out this. Okay, This angle we have to find out without this angle were unable to solve this. Okay, let them this angle. B X So if this will be acts by alternate angles, this will also x Okay, so from course Cheetah missed by course X Uh, this is 435 We will get the value for by fight, so acts will be course in words for by five that is Tartus 6.86 degree. This is the value effects if you add this, uh, if you add the value off packs in this 90 degree, you will get the angle between this FC and Absi, That is Pita is 90 plus acts that is 90 plus touch his 6.86 diggy. That is 1 26 point air 60. Okay, now we know in the next Resultant is Bangu. Have fun square plus have to square plus two Afghan after course. Okay, so here, after one is at sea, a square blurs FCB square plus toe at C A F C B course 1 26.86 degree. Okay, thank you. If you will put all the values here that is 30 neutral square last 21.6 Newtown Square. Let's two in tow tarty into 21.6 into minus 0.59 Okay, this is a value off course. 1 26.8 60 Okay, By solving this, you will get an approximate answer off, resulting fourth, 24.4 newton. This is the next result and force on sea by D's to tow A and B. And this is in the direction. This way. Okay, well, this is all for me for this video. I hope you will like the video. Thank you.

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