MHB Analyzing Electromagnetic Forces in a Two-Sphere System with Insulating Fiber

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The discussion focuses on analyzing the forces acting on two positively charged plastic spheres sliding along an insulating fiber. Each sphere has a mass of 0.1g, with one sphere positioned 6 cm above the other. The repulsive electric force between the spheres can be calculated using Coulomb's Law, despite initial confusion about the lack of a given force. To maintain the upper sphere's position, an additional force must counteract the repulsion, and participants are encouraged to determine the angle of the fiber needed to double the separation while keeping the charges constant. The conversation emphasizes the interplay of electric forces and the need for a comprehensive analysis of the system.
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the two small plastic spheres are arranged so that they can slide freely along the insulating fiber. Each has a mass of 0.1g. The spheres are given identical positive charges. a. If the lower sphere is resting against the lower knot while the upper sphere moves to a location 6 cm distant from that knot, find the charge on each. b. if the charges remain the same, what angle should the fiber make with the horizontal to double the separation?

can you help on this problem. I'm having a hard time analyzing it. There's no given force(repulsive) I can't seem to use coulombs law here. please help!
 

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Each of the plastic spheres repels the other, since they are both positively charged-this is why one of the spheres moves 6 cm up the fiber. Therefore, the third-law pair here is electric force with electric force, and you can use Coulomb's Law.
We also need another force, one that keeps the higher bead from moving away further than 6 cm. So, what do you think you should do now?
 
Thread 'Erroneously finding discrepancy in transpose rule'

Thread 'Erroneously finding discrepancy in transpose rule'

Obviously, there is something elementary I am missing here. To form the transpose of a matrix, one exchanges rows and columns, so the transpose of a scalar, considered as (or isomorphic to) a one-entry matrix, should stay the same, including if the scalar is a complex number. On the other hand, in the isomorphism between the complex plane and the real plane, a complex number a+bi corresponds to a matrix in the real plane; taking the transpose we get which then corresponds to a-bi...
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