How Do You Calculate Charge Magnitude Using Coulomb's Law?

[HobieDude16]

ok, I am trying to do this "prelab" thing for my lab tomorrow, and there is one question i just can NOT figure out. the question is

The weight of a 0.6 kg object of charge Q is just balanced by another object of equal but opposite charge fixed to a support 107 cm above it. What is the magnitude of the charge Q (in μC)? [Note that 1 μC=1x10-6C.]

i understand how coulomb's law works, with F=k(q0q1)/r^2 but what i am having trouble figuring out, is what can i do to get an answer here? i have the mass, and the distance (r). i was thinking to use the force of gravity formula, and set it equal to coulomb's, but i looked at an example in the book where they are given q0 and q1, and they found both gravity and coulombs, and the answers were not equal. so i figured that must mean that is not the right way to do it...

any ideas? sorry so long, its been bugging me for a while now... any help is appreciated

thanks in advance

 

[cepheid]

The weight of a 0.6 kg object of charge Q is just balanced by another object of equal but opposite charge fixed to a support 107 cm above it. What is the magnitude of the charge Q (in μC)? [Note that 1 μC=1x10-6C.]

It tells you that the object's weight is just balanced by the electric force on it from the opposite charge. You already know the object's weight, right? So from that and Coulomb's law you can easily calculate the required equal and opposite electric force to balance it.

 

[quicknote]

Hello,

Thank you for reaching out. It seems like you are on the right track with using Coulomb's law to solve this problem. You are correct in thinking that you can use the force of gravity formula to set up an equation with Coulomb's law. However, the example in the book where the answers were not equal may be due to the fact that the objects in that example were not balanced, unlike in this problem where the weight of one object is balanced by the opposite charge of the other object.

To solve this problem, you can set up an equation using Coulomb's law: F = k(q0q1)/r^2, where F is the force of gravity and k is the Coulomb's constant. Since the objects are balanced, the force of gravity must be equal to the force of the electric field, so you can set the two equations equal to each other: mg = k(q0q1)/r^2. From there, you can solve for q0, which will give you the magnitude of the charge Q in μC.

I hope this helps and good luck with your lab tomorrow! Let me know if you have any other questions.