Daniel B. answered • 01/21/23
A retired computer professional to teach math, physics
If you are planning an actual experiment, you need to make sure that the
mass of the string is negligible in relationship to the tape.
Otherwise the string would be bent, and it would be much more complicated.
I would suggest using a thread instead of a string, and adding a weight to the tape.
Whatever you do, from now on I am assuming that the mass of the string is negligible.
Also you do need to know the mass of the tape, because the displacement
depends also on the mass, not just the charge.
The calculation is easiest if you can hold the other piece of tape
so that it is horizontally from the piece of tape attached to the string.
The calculation is more complicated if you held your tape at the original
relaxed end of the string.
Let
m be the mass of the tape,
L = 40 cm be the length of the string,
Q (to be calculated) be the charge on each piece of tape,
d be the distance between the two pieces of tape,
α be the angle between the string and the vertical,
g = 9.81 m/s² be gravitational acceleration,
k = 9×109 Nm²/C² be Coulomb's constant.
Please draw a picture.
The tape attached to the string is subject to three forces:
mg -- vertical force of gravity,
kQ²/d² -- horizontal electrical force,
force of tension along the string.
As the tape is not moving, the vector sum of those three forces is 0.
For that, the vector sum of the force of gravity plus the electrical force
must form the same angle α with the vertical.
Therefore
tan(α) = (kQ²/d²)/mg
From the triangle formed by the string with the tape you are holding
tan(α) = d/√(L²-d²)
This gives you the equation
(kQ²/d²)/mg = d/√(L²-d²)
from which you can calculate Q.
