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Two uniformly charged spheres are firmly fastened to andelectrically insulated from frictionless pucks on an airtable. The charge on sphere 2 is three

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asked 2021-05-06
Two uniformly charged spheres are firmly fastened to andelectrically insulated from frictionless pucks on an airtable. The charge on sphere 2 is three times the charge onsphere 1. Draw the force diagram that correctly showsthe magnitude and direction of the electrostatic forces. Explain your reasoning.

Answers (1)

2021-05-08
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Let "R" be distance between Sphere centers. Then vector Force "\(\displaystyle{F}_{{1}}\)" on Sphere #1 is equal & opposite to vector Force "\(\displaystyle{F}_{{2}}\)" on Sphere #2:
\(\displaystyle{F}_{{1}}=-{F}_{{2}}\)
The Spheres REPEL each otherbecause they each contain the SAME-SIGN charge. Thus, using Coulomb's Law:
\(\displaystyle\text{Magnitude }\ {F}_{{1}}=\text{Magnitude }\ {F}_{{2}}={\frac{{{1}}}{{{4}\cdot\pi\cdot\epsilon_{{0}}}}}\cdot{Q}\cdot{\frac{{{3}\cdot{Q}}}{{{R}^{{2}}}}}\)
Direction \(\displaystyle{F}_{{1}}\)=OPPOSITE Direction \(\displaystyle{F}_{{2}}\)
{Sphere #1 &Sphere #2 REPEL Each Other}
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