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*example included* Two uncharged spheres are separated by 3.50 m. If 1.30 ✕ 10¹² electrons are removed from one sphere and placed on the other, determine the magnitude of the Coulomb force (in N) on one of the spheres, treating the spheres as point charges. Find the net charge on each sphere and substitute values into Coulomb's law.

*example included* Two uncharged spheres are separated by 3.50 m. If 1.30 ✕ 10¹² electrons-example-1
User Bryan Ruiz
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1 Answer

3 votes

Answer:

  • 3.18283×10^-5 N
  • 2.08283 C

Step-by-step explanation:

You want the force and net charge on one of two spheres separated by 3.5 m if 1.30×10^12 electrons are removed from one of the uncharged spheres and placed on the other.

Charge

Each electron is 1.602177×10^-19 coulombs (C), so 1.3×10^12 of them is a charge of ...

(1.602177×10^-19 C/electron) × (1.30×10^2 electrons) = 2.08283×10^-7 C

The net charge on each sphere is about 2.08283×10^-7 coulombs.

Force

The force between the spheres is given by Coulomb's Law:

F = kQq/r²

where Q and q are the charges separated by distance r. The value of k is Coulomb's constant, equal to 1/(4πε₀) ≈ 8.98755×10^9 Nm²/C².

The force between the spheres in the given setup is ...

F = 8.98755×10^9 × (2.08283×10^-7/3.5)² ≈ 3.18283×10^-5 N

The magnitude of the Coulomb force is about 3.18283×10^-5 N.

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Additional comment

The various constants involved here can be found rounded to various numbers of significant figures. Here, we have elected to use the "full precision" values provided by NIST, rounding the results shown to 6 significant figures. As a practical matter, 3 significant figures are usually sufficient for comparison to anything you can measure. (The given values have 3 sf, so your answer should probably be rounded to that precision.)

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User Axel Andersen
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