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