Peoples Physics Concepts

http://www.ck12.org Chapter 12. Electricity

Example 1

Question: Two negatively charged spheres (one with− 12 μC; the other with− 3 μC) are 3m apart. Where could you
place an electron so that it will be suspended in space between them with a net force of zero (for this problem we
will ignore the force of repulsion between the two charges because they are held in place)?

Answer: Consider the diagram above; herers→eis the distance between the electron and the small charge, while
~Fs→eis the force the electron feels due to it. For the electron to be balanced in between the two charges, the forces
of repulsion caused by the two charges on the electron would have to be balanced. To do this, we will set the
equation for the force exerted by two charges on each other equal and solve for a distance ratio. We will denote the
difference between the charges through the subscripts "s" for the smaller charge, "e" for the electron, and "l" for the
larger charge.

kqsqe

r^2 s→e

=

kqlqe

re^2 →l

Now we can cancel. The charge of the electron cancels. The constantkalso cancels. We can then replace the large

and small charges with the numbers. This leaves us with the distances. We can then manipulate the equation to

produce a ratio of the distances.

− 3 μC

rs^2 →e

=

− 12 μC

r^2 e→l

⇒

rs^2 →e

r^2 e→l

=

− 12 μC

− 3 μC

⇒

rs→e

re→l

=

√

1 μC

4 μC

=

1

2

Given this ratio, we know that the electron is twice as far from the large charge (− 12 μC) as from the small charge

(− 3 μC). Given that the distance between the small and large charges is 3m, we can determine that the electron

must be located 2m away from the large charge and 1m away from the smaller charge.

Watch this Explanation

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