How is the tension in the string related to the electric force on a pith ball?

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SUMMARY

The tension in the string T, holding a pith ball of mass m and positive charge q, is directly related to the electric force F exerted by a positive charge Q located at the origin. At equilibrium, the pith ball remains stationary, forming an angle θ with the vertical y-axis while being a distance L from charge Q. The tension can be expressed as T = F + mg cos(θ), where mg represents the gravitational force. Additionally, the charge q on the pith ball can be expressed in terms of m, θ, L, Q, and constants such as the gravitational acceleration g.

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  • Basic principles of equilibrium in physics
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mich_v87
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A positive charge Q is located at the origin.A small pith ball of mass m and positive charge q is attached to a light string and hangs from a point on the y-axis above the origin.The length of the string is.The teo posotove charges repel,and at equilibrium the pith ball is stationnary with the string making an angle θ to the y-axis, and with the pith ball being a distance L from Q,as shown in the sketch below.
1-Express the tension in the string T in terms of the electric force F on the pith ball and possibly other quantities
2-Express the charge q on the pith ball in terms of m,θ,L,Q and possibly other constants.

p-4.JPG
 
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