Why Does Charge Q Not Appear in the Equilibrium Equation for Helium Balloons?

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SUMMARY

The equilibrium of two small helium-filled balloons, each with charge "Q", tied to a 50g weight, is analyzed. The total force on each balloon is zero, leading to the conclusion that the electrostatic forces between the balloons cancel each other out. The key insight is that the horizontal forces include the electrostatic repulsion and the tension in the strings, which must balance to maintain equilibrium. Understanding this balance is crucial for solving the problem accurately.

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shaiqbashir
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HI Guys!

Please help me in solving this simple problem. I am getting an answer which is not matching with the answer given in my book. The problem is:

"TWO SMALL HELIUM FILLED BALLONS, TIED TO A 50gm WEIGHT FLOAT IN EQUILIBRIUM.(TOTAL FORCE ON EACH BALLOON IS ZERO). EACH BALLOON HAS A CHARGE "Q". FIND "Q".
See attached fig also:

now i have tried it many times. what I am confusing that suppose i take one ballooon under consideration. Then the force that is exerted by the second balloon on the first one and the force exerted by the 1st on the second will cancel each other. so there would be no expression left with the term "Q".

Please help me, i have a very short time.

Thanks in advance!
 

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Take a single balloon. Note that the horizontal forces on this balloon include the electrostatic force and a component of the tension in the string, and that the horizontal forces sum to 0.
 
An approach: If instead of balloons you just had the mass hanging from two ropes, could you find the tension in the ropes? If you can do that, you will know that the ropes are pulling the two balloons together. The repulsion is counteracting the force pulling them together.
 

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