Question

How would you design an experiment to precisely measure the force and the position of charges and verify Coulomb's law for electrostatics? Briefly note what the problems are with the one you did and then offer ideas on ways it could be done precisely.

please answer both parts

Answer 1

Designing an experiment is never an easy task and thinking about it in just a span of 10 minutes isn't easy too but I also had a thought about it and i was fascinated by mullikan's oil drop experiment to find the charge of an electron, was the idea for me to think ..

Similar to oil drop experiment, I would have two fixed charged entities and keep them as small as possible to be sure that the charge is confined to a small sphere as possible ,so that i could assume it to be a point charge ,fix one of the charges and insulate it so that the body does not leak charge and then use a lightweight tention wire to tie the other charge ,bring the charge from a good height so that we are sure that gravitational force is more than electrostatic force and resultingly the tention in the wire would be positive ,in a line bring the charge down and then keep brining it down until the tention in the wire gets down to zero ,at that point electrostatic force would equal the gravitational force and since the charges were fixed we could verify the law to find the value of k.

The major problems i feel to face would be getting a charged entity so small to be considered as a point charge is very difficult and the position of the charge would surely be defined in this case since there is only a single distance possible here , to be able to identify the distance what we can do is take the difference of gravitational force and tention at any position and equate it to the electrostatic force and get the distance theoritically from there and then measure using some scales the distance of both the particles

One more of the problem one might face is that we might get errors if performing this experiment in air ,since air has charged ions too it might cause some minor errors to possibly occur and the thread wire through which the charge would be attached should ideally be weightless

One error one might do is neglect gravitational force of charged bodies ,when taking the total gravitational force on the body .

This is what i would like to experiment
Feel free to share your views over this and comment what error you think there might be , we might come up with something interesting.
Thank you