Interactive Lecture Demonstration E1 – Charged Balloons and Coulomb's Law

 

A balloon, hanging from a string, will be charged by rubbing it with rabbit fur (one of the most electropositive substances known – this means that rabbit fur becomes positively charged by losing electrons to almost any object that you rub with it). A second balloon will be rubbed with rabbit fur and brought near the first one. The two balloons will repel each other due to the Coulomb (electrostatic) force of each on the other.

 

This ILD will be a good test of your ability to solve problems using Newton's Second Law – i.e. force diagram problems. You should have already read the Complete Guide to Perfect Force Diagram Solutions handout describing the procedure for solving those problems. We will follow that procedure in this ILD.

 

The purpose of this ILD is to determine the number of electrons that were rubbed on to each balloon (we will assume that the rabbit fur transferred the same number of electrons to each balloon).

 

  1. Before beginning our calculation, estimate how many electrons you think were transferred to each balloon by the rabbit fur. You should be able to guess the order of magnitude (power of ten) of the number, based on information found in today's reading. Write your guess below:

 

 

  1. Below is a diagram of the hanging balloon when the second balloon (not shown) is brought near it. D is the center-to-center distance from the hanging balloon to the second balloon. θ is the angle that the string makes with the vertical. Estimate (or measure) D, θ and the balloon's mass, and write your estimates next to the diagram. These will be our given information for the problem. (step 1 in the Complete Guide)

 

 

 

                                                                                

 

 

 

 

                                      

 

 

                                         

                                              

 

 

 

 

 

 

 

 

  1. Draw a force diagram for the hanging balloon when the second balloon is brought next to it (but not touching). What is the net force on the balloon when it hangs in equilibrium ? Check to make sure that your force diagram is consistent with what you know the net force to be. (step 2 on the Complete Guide)

 

 

 

 

 

 

 

 

 

  1. We hope you realized that the net force on the hanging balloon is zero. Now you need to write the net force equations for the balloon. But first, you must define two mutually perpendicular positive directions, and determine the vector components of all the forces along those two directions. Show below your choice of positive directions and your vector diagrams to break up any forces that have more than one component. Note that you can make your work easier by choosing your positive directions so that you need vector diagrams for the fewest number of forces. (steps 3,  4 and 5 in the Complete Guide)

 

 

 

 

 

 

  1. Now write the net force equations, one for each of your two perpendicular directions. (step 6 in the Complete Guide)

 

 

 

 

 

 

 

 

 

 

  1. We want to know the number of excess electrons on the hanging balloon (let's call that N). This is related to the total excess charge Q of one of the balloons (remember, we are assuming that both balloons have the same excess charge). Write a formula to find N in terms of Q.

 

 

  1. Now do the algebra to find a formula for N only in terms of the given quantities for this problem and the physical constants k (constant in Coulomb's Law), g (Earth's gravitational field) and e (charge of a proton). (step 7 in the Complete Guide). Your final result should be:

 

N = D/e * √ mg tan(θ)/k

 

 

 

 

 

 

 

 

  1. Now substitute numbers (with units) into your formula for N to get your result. How does it compare with your prediction in part 1 ? (step 9 in the Complete Guide)