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# Two small beads having positive charges $q_{1}=3 q$ and $q_{2}=q$ are fixed at the opposite ends of a horizontal insulating rod of length $d=1.50 \mathrm{m}$ . The bead with charge $q_{1}$ is at the origin. As shown in Figure $\mathrm{P} 15.66,$ a third small charged bead is free to slide on the rod. At what position $x$ is the third bead in equilibrium?

## 0.951 $\mathrm{m}$

### Discussion

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##### Top Physics 102 Electricity and Magnetism Educators  ##### Christina K.

Rutgers, The State University of New Jersey ##### Andy C.

University of Michigan - Ann Arbor

LB

### Video Transcript

Harris train Sledge died or discussion. Suppose you have a slight off road. Okay? No, Both the ends that is. Beads are two charges Q one and Q toe our line and the value off to one that is magnitude ask you. One is take you and the magnitude of Q two is you. Another charge. Q is free to move inboard direction and we have to find out the You're three do trees published? No, we have to find other dispense X at fridge. The electric field on this charge is Jiro. The total distance between charge Q one and Q two is these okay? And the value off B is 1.5 meter. We have to find out the X so basically electric field on this position from if I have named them one three. Okay, so electric field on three due to one is in this direction. An electric failed on fee due to two is in this direction solve. If both fields are equal, then only discharge country is in equilibrium position. So e three to magnet tool off this charge will be magnitude off eat even also, basically, it will be okay cure toe by B minus exc a whole square and 81 will be okay. You won B o x horse crap. Okay, so I gave it begins load and it will be cute by Q one d minus acts upon x Whole square value off Q two is que and value off Q one is trick you. So it really big d minus acts upon x whole square. So from here, you will be cancel out implies one upon route three B minus acts upon x so by a soldering this we will get here acts route three D minus 43 x and one of blessed would be x three d. So actually comes Toby. Look. 31 plus room three. And the value off the is one point five meter. So my soul in this, we will get a value off 0.95 meter. Well, this is all from me for this video. I hope you will like the video. Thank you. Other Schools
##### Top Physics 102 Electricity and Magnetism Educators  ##### Christina K.

Rutgers, The State University of New Jersey ##### Andy C.

University of Michigan - Ann Arbor

LB