Peoples Physics Book Version-2

http://www.ck12.org Chapter 13. Electricity Version 2

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

r^2 s→e

=

− 3 μC

r^2 e→l

⇒

r^2 s→e

r^2 e→l

=

− 12 μC

− 12 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
(− 12 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.

Electric Fields and Electric Forces

Gravity and the Coulomb force have a nice property in common: they can be represented byfields. Fields are a kind
of bookkeeping tool used to keep track of forces. Take the electromagnetic force between two charges given above:

~Fe=kq^1 q^2

r^2

If we are interested in the acceleration of the first charge only — due to the force from the second charge — we can
rewrite this force as the product ofq 1 andkqr 22. The first part of this product only depends on properties of the object
we’re interested in (the first charge), and the second part can be thought of as a property of the point in space where
that object is.

In fact, the quantitykqr 22 captures everything about the electromagnetic force on any object possible at a distancer

fromq 2. If we had replacedq 1 with a different charge,q 3 , we would simply multiplyq 3 bykqr 22 to find the new force
on the new charge. Such a quantity,kqr 22 here, is referred to as the electric field from chargeq 2 at that point: in this
case, it is the electric field due to a single charge:

E~f=kq

r^2

[2] Electric field due to point chargeq,distanceraway