In the following steps we find the number of excess electrons.Step 5 shows that a miniscule amount of charge í about a ten-thousandth of the charge you transfer to a balloon when you rub it on your shirt
í is enough to balance the gravitational attraction between two one-kilogram masses separated by one meter. If you were concerned about
whether adding the excess electrons would alter the mass of each sphere enough to require recalculating their gravitational attraction, you can
compute that they add an insignificant mass, about 5×10í^22 kg, to each sphere.
As an additional exercise, you can use Avogadro’s number, and the atomic weight and atomic number of lead, to find the total number of
electrons in an uncharged kilogram of lead. This calculation is not shown, but the total number is 2.39×10^26 electrons. This means that the
excess electrons constitute about 10í^16 percent of the electrons in the sphere.Step Reason
6. q = –Ne equation for charge
7. solve for N
8. evaluate
22.10 - Interactive checkpoint: electric vs. gravitational force
Compute the ratio of the electric to
the gravitational force between the
proton and electron in a hydrogen
atom. Use the average distance
between the two, which is called the
Bohr radius and equals 5.29×10í^11 m.
Answer:FE/FG =
22.11 - Superposition of electrostatic forces
Electrostatic forces obey the principle of superposition. The forces caused by multiple
charges can be added as vectors. For instance, consider the charges shown in Concept- To calculate the net force exerted by the other charges on the charge labeled q 1 , the
forces exerted by q 2 and q 3 on q 1 are individually calculated and then those two forces
are added as vectors. In the next section, we solve a sample problem involving charges
that requires the use of this principle.
You must be careful about the directions of electrostatic forces, especially when
combining forces that may point in opposite directions. The location and signs of the
charges determine the direction of the forces.
For example, consider another set of charges, q 4 ,q 5 , and q 6 , with all the charges on a
line, and q 6 the rightmost charge. Let’s say charges q 4 and q 5 have opposite signs.
Since both are on the same side of q 6 , the forces they exert upon it will act in opposite
directions. There will be cancellation and the net force will be less than the sum of the
magnitudes of the individual forces. There is no “rocket science” here. Just be careful to
consider the direction of forces before combining them.Electrostatic forces: vectors
Electrostatic forces are vector quantities
Net force = vector sum(^410) Copyright 2000-2007 Kinetic Books Co. Chapter 22