Conceptual Physics

Variables

What is the strategy?

1. Calculate the gravitational attraction between the lead spheres.


2. Set the gravitational force equal to the repulsive electrostatic force between them and solve for the charge. The amount of charge on
   each sphere is the same.


3. Convert the charge from coulombs to the equivalent number of excess electrons.

Physics principles and equations

We will use Newton’s law of gravitation

together with Coulomb’s law

The charge due to N excess electrons is

q = íNe

Step-by-step solution

In the first steps, we calculate the charge q needed on the spheres to balance their gravitational attraction.

sphere 1 sphere 2

mass of sphere m 1 = 1.00 kg m 2 = 1.00 kg

charge of sphere q 1 q 2

gravitational constant G = 6.67×10í^11 N·m^2 /kg^2

distance between spheres r = 1.00 m

gravitational force on sphere Fg

electric force on sphere Fe

Coulomb’s constant k = 8.99×10^9 N·m^2 /C^2

number of excess electrons N

elementary charge e = 1.60×10í (^19) C

Step Reason

1. Newton’s law of gravitation

2. evaluate

3. set forces equal and use Coulomb’s law

4. solve for q

5. note electron charge negative and evaluate

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