Estimating the Ratio of theta1 & theta2: Two Spheres with Unequal Charges

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The discussion centers on estimating the ratio of angles theta1 and theta2 for two charged spheres, S1 and S2, which are influenced by their charges and masses. Despite S2 having double the charge of S1, the angles remain equal due to the equal lengths of the strings and the horizontal alignment of their attachment points. Participants question the implications of differing charges on the forces between the spheres, referencing Coulomb's law and Newton's third law. It is clarified that while the forces are unequal, the equilibrium conditions lead to the same angle of inclination for both spheres. Ultimately, the estimated ratio of theta1 to theta2 is confirmed to be 1.
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Two spheres S1 and S2 hang from light insulating strings of the same length from points P1 and P2 which are on the same level. S1 is of mass M and has charge Q. S2 is of mass M and has charge 2Q. Repulsion between S1 and S2 causes their strings to be inclined at angles of theta1 and theta2 to the vertical respectively. What is the estimated ratio of theta1/theta2?
The ans is 1.
Is it because P1 and P2 are on the same level and the two strings are of the same length?
But the charges of the two spheres are different. Shouldn't one of them be repelled further?
 
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What is the magnitude of the force from S1 to S2, and what is the magnitude of the force from S2 to S1?
 
The force from S2 to S1 should be double that of the force from S1 to S2 because S2 has charge 2Q??
 
Have another look at Coulomb's law and compare the 2 electric forces.
Also think about Newton's 3rd law.
 

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