When you rub part of a rubber balloon against wool (or your hair), electrons will leave the wool, which is slightly conductive, and go onto the balloon. The rubber on the balloon is much less conductive (rubber is more of an insulator than wool), and the electrons will not readily leave the balloon. As a result, the balloon becomes negatively charged. Imagine you bring the negatively charged balloon up to a wall, and it sticks (This is possible! A quick internet search will yield many explanations and demonstrations. You can also try it yourself). Why would the balloon stay in one place on the wall? Draw a free body diagram for the balloon to help your explanation.

• The balloon is negatively charged.
• The balloon is stuck to the wall.

• Find a way to explain why the balloon sticks to the wall.

We observe the balloon stuck motionless to the wall. If we want to draw a free body diagram to analyze the forces, we know that the net force must be zero. If we had to list out the forces, we could start with gravity. That will point straight down. Also, since the balloon is up against the wall, there must be a normal force from the wall, too. To simplify our model, we make an assumption:

The only force we could have is the electric force between the balloon and the wall. Since the net force on our balloon is zero, the free body diagram looks something the following representation:

• The balloon is not very conductive, so the electrons from the wool are stuck where they are. We'll say they are distributed near the part of the balloon close to the wall.
• The wall is a perfect insulator, and is neutral.
• There is no friction between the wall and the balloon. (This assumption is not necessary! Depending on what you think of the other forces at play, friction may or may not play a role. For our solution, we do not use friction.)
• The interaction between the wall and the extra negative charges on the balloon is much stronger than the interaction between the wall and any polarized atoms in the balloon. For this reason, we choose to ignore polarized atoms in the balloon. This seems reasonable, since a balloon will not stick to a wall without having rubbed the balloon with something that will transfer some of its electrons to the balloon.

Based on our Approximations and Assumptions, we can draw the following diagram of the (motionless) situation: We know that the balloon is negatively charged from rubbing it on wool/hair. When we bring the charged balloon close to the wall, the atoms in the wall near to the balloon become polarized with the electron clouds being pushed away from the negative balloon. See the notes on Charges and Matter for more information on polarization. This means that negative balloon is now attracted to the positive nuclei in the polarized wall.

We know the balloon is motionless, so air resistance is not a factor here, as it often is with balloons. Also, because the balloon is motionless, the net force is zero so all of our forces must cancel out. We know we have a gravitational force from the earth, a normal force from the wall, and an attractive electric force from the wall. That is all! Notice that the electric force needs to point both to the left and upward in order for the net force to be zero. If you were to try this experiment out yourself, you may notice the balloon rolling slightly up and down (oscillating) before settling to a motionless state. As the balloon rolls, the charge distribution on the balloon moves with respect to the wall, which changes the direction of the electric force on the balloon from the wall. When the balloon settles, we know it has come to a place where the direction and magnitude of the electric force results in a net force of zero. A force diagram on the motionless balloon is shown below.

Note on friction: We do not include friction in the force diagram. We assume the electric force has enough of an upwards component that friction contributes nothing. However, depending on assumptions that you make, you may have friction in your force diagram. In reality, there is probably both friction and a slightly upwards electric force component at play here.