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If two charged bodies are connected by a string will the tension be F or 2F?(F is the force of repulsion between them)

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marked as duplicate by garyp, user36790, Qmechanic Nov 27 '16 at 17:24

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  • $\begingroup$ There will be Tension $T=F$ from both sides of the string, on each side where the charges are attached. However. I do wonder what the total force experienced by the string is. 2F or zero? $\endgroup$ – Kalpak Gupta Nov 27 '16 at 15:42
  • $\begingroup$ Net force on the string is zero. Tensile stress at any point in the string is $F/A$ with $A$ the cross section of the string. $\endgroup$ – Pirx Nov 27 '16 at 15:55
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    $\begingroup$ Possible duplicate: physics.stackexchange.com/q/41291/50583 $\endgroup$ – ACuriousMind Nov 27 '16 at 15:59
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If the electrostatic repulsive force is given by $$F=\frac{Q_1Q_2}{4\pi\epsilon_0r^2}$$ and you consider one body held back by the string, the force exerted by the string on the body will be $-F$ so that there is a zero total force on the body. Thus, according to Newton's 3rd law, at any cross section of the string the sum of the positive and negative force $F$ gives a zero total force $F_\textrm{tot}=F-F=0.$ Thus the tension in the string is simply the repulsive force $F$ between the bodies

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  • $\begingroup$ This is a good answer. The key to getting this right is to consider each body separately, and accounting for the force on each. But note that things are different if the string has mass. But in most introductory problems, the string is massless. $\endgroup$ – garyp Nov 27 '16 at 16:41
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The tension will be F because supposing you only had one of the charged bodies, there would be no tension. You have to look at it as though it is pulling from one side, don't look at it from both perspectives. The tension is being produced from one side.

For more explanation and verification look here:

https://www.physicsforums.com/threads/find-tension-in-string-connecting-two-charged-spheres.696711/

https://www.quora.com/What-is-the-tension-on-string-connecting-two-charged-spheres

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