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

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SUMMARY

The discussion centers on the estimation of the ratio of angles theta1 and theta2 for two charged spheres, S1 and S2, with unequal charges. Sphere S1 has a charge Q and sphere S2 has a charge 2Q, both suspended from equal-length strings. The conclusion reached is that the ratio theta1/theta2 equals 1, attributed to the equal lengths of the strings and the same height of attachment points P1 and P2. The forces acting between the spheres are analyzed through Coulomb's law and Newton's third law, confirming that the forces are indeed equal in magnitude despite the difference in charge.

PREREQUISITES
  • Understanding of Coulomb's law for electric forces
  • Familiarity with Newton's third law of motion
  • Basic knowledge of trigonometry related to angles and forces
  • Concept of equilibrium in physics
NEXT STEPS
  • Review Coulomb's law and its application in electric force calculations
  • Study Newton's third law in detail, focusing on action-reaction pairs
  • Explore the principles of equilibrium in systems with multiple forces
  • Investigate the effects of varying charge magnitudes on force interactions
USEFUL FOR

Physics students, educators, and anyone interested in understanding electrostatics and force interactions in charged systems.

iknownth
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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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