# Why was it necessary for Coulomb to invent his torsion balance while we can measure force using a spring balance?

Just like we measure the force due to masses using spring balance, we can also measure the force between two charges by using a spring balance.

What was the need for Coulomb to invent his torsion balance for measuring the force between two charges while we can easily measure the force between two charges by using a spring balance?

EDIT

If we say we can measure gravitational force to a good precision using a usual spring balance because the earth is very very large and we cannot measure electrostatic force to a good precision using a usual spring balance because the charge in lab is small, then we must notice that we are measuring force and not size.

The gravitational force on my chair due to earth is almost as same level as force between two charged balls in a laboratory. Since the former can be measured with good needed precision using spring balance, why cannot we do the same for latter? What am I misunderstanding?

EDIT 2:

I stated: "The gravitational force on my chair due to earth is almost as same level as force between two charged balls in a laboratory." Is this statement wrong? By almost as same level, I mean the force on chair is "about 25 or less times" larger than force between charges.

• You must have a really really good spring balance then. A torsion balance is far more sensitive. Dec 31, 2022 at 4:39
• We can measure gravitational force to a good precision using a normal usual spring balance. So why can't we measure electrostatic force to that precision level using a usual spring balance? Dec 31, 2022 at 4:43
• Because the Earth is quite large. Now try to measure the gravitational force that one 1 kg object exerts on another 1 kg object. Dec 31, 2022 at 4:46
• In that case the force would be too small for a normal spring balance to measure. But notice that we are measuring force and not size. The gravitational force on 1kg object due to earth is almost as same level as force between two charged balls in a laboratory. Since the former can be measured with good needed precision using spring balance, why cannot we do the same for latter? What am I misunderstanding? Can anybody explain in an answer? Dec 31, 2022 at 5:06
• I stated: "The gravitational force on my chair due to earth is almost as same level as force between two charged balls in a laboratory." Is this statement wrong? By almost as same level, I mean the force on chair is "about 25 or less times" larger than force between charges. Dec 31, 2022 at 7:09

It is difficult to create a large charge on a spherical object because the self capacitance of a sphere is relatively small so even a small charge produces a large voltage. That large voltage causes the charge to flow to ground fast unless the resistance of the sphere and support is very, very high, and even them the charge will slowly leak away into the air around the sphere.

That means to get a charge that remained constant long enough to perform the experiment Coulomb had to work with small charges and therefore small forces. This requires a very sensitive force balance and a torsion balance is ideal for this.

In principle a spring balance could have been used, but it is very hard to make a spring balance as sensitive as a torsion balance.

For anyone interested there is a description of Coulomb's experiment here.

• Thank you... I understand... But how did Coulomb prove the superposition principle. Dec 31, 2022 at 8:28
• Is there a way to prove the superposition principle? Or shall I ask it as a separate question? Dec 31, 2022 at 8:29
• @lorilori Do you mean show that electrostatic forces sum linearly? Dec 31, 2022 at 8:30
• Yes, I mean to verify...... The force on a charged ball is the vector sum of forces due to individual charges Dec 31, 2022 at 8:31
• Yes, you can calculate the torque on the balance as $\tau = \sum \mathbf r \times \mathbf F$ where the sum is over all the charged balls. It does mean you need to measure both the distance between the ball and the balance and the angle the line from the ball to the balance makes with the balance arm. Dec 31, 2022 at 8:46