Answers for E1 (rev. 3.0)
E-1. Coulomb’s Law
Questions for discussion
1. Coulomb’s Law for the electrostatic force between two point charges is
F = qQ 4"#
r2 . (ε0 is
constant, equal to 8.85×10-12 C2/N⋅m2, which determines the relative strength of the electric force.
Some texts use the constant kC = 1/4πε0, called Coulomb’s constant instead, which makes Coulomb’s
Law look even more like Newton’s law of gravitation!) This looks a lot like Newton’s law for the
gravitatational force between two point masses:
F = G mM r
2 . And indeed, because both forces are
“1/r2 forces,” there are some mathematical similarities between them.
However, all similarities aside, can you think of any important differences between electrostatic
forces and gravitational forces?
Perhaps the most important difference is that gravitational forces are always attractive, whereas
electrostatic forces can be attractive or repulsive.
2. Two point charges q1 = +2 C and q2 = -3 C are fixed in place along the x-axis, as shown.
You have in your hand another point charge q, and you want to place it somewhere on the x-axis.
But you want to place it at a point where it will stay. That is, you want to place it at a point where
it will feel no force due to the fixed charges q1 and q2. (Hint: Think about what the force looks like
very close to each charge and what it looks like very far away from both charges.)
a) Is there any point on the x-axis in between the two fixed charges, where you could place your
charge q and it would remain at rest? Explain. Does you answer depend on whether your charge q
is positive or negative? Why or why not?
There is no point between the two fixed charges where your added charge q would remain at rest. This
is because the +2 charge and the -3 charge both exert forces on q in the same direction. (If q is
positive, then both forces are to the right. If q is negative, then both forces are to the left.) Hence the