# Exploring Electric Force: Guidance with Mastering the Basics

- Let's delve a bit deeper into the history of Coulomb's Law:

Charles-Augustin de Coulomb was a French physicist and engineer. Born in 1736, he had a keen interest in various scientific fields, including mechanics and electricity.

In the 18th century, there was a growing interest in understanding the nature of electricity. Scientists like Benjamin Franklin (**First scientist who discovered the concept of electric charge**) were making significant contributions, and the concept of electrical charge and its effects were becoming increasingly explored. Then he thought I have to do an experiment with two charged objects .

**1.1 Coulomb's Experiments:****

In the mid-1780s, Coulomb began conducting a series of experiments to investigate the forces between charged objects. His experiments were meticulous and involved using a torsion balance, a device that measures the torque or twisting force.

**1.2 Torsion Balance:****

Coulomb's torsion balance consisted of a horizontal bar suspended by a thin wire. At each end of the bar, small charged spheres were attached. The bar could twist due to the electric forces between these spheres. While doing experiments he realized that only the integer value of a charged particle can exist.

**1.3 Quantifying Electric Force:**

Coulomb wanted to quantify the force between charged objects, and he developed a method to do so. By measuring the angle of twist and knowing the properties of the wire, he could relate the twisting force to the electric force between the charges. By doing this experiment he observed these are things .

**1.4 Observations:**

Through systematic experimentation, Coulomb made several key observations. He found that the force between charges was directly proportional to the product of their charges (**It means when we increase both charges by two units Then force will increase upto 4 units**) and inversely proportional to the square of the distance between them (**It means when we increase distance between two charged particles by two unit then the force between the charge particle degrees by 2 units**). This empirical relationship formed the basis for Coulomb's Law.

Coulomb wants to prove our theorem by mathematical approach so he begins to find out how to write in mathematical approach.

**Coulomb's Law Formula**

**Coulomb's Law Formula**In 1785, Coulomb presented his findings in a paper titled "**Premier MÃ©moire sur l'Ã‰lectricitÃ© et le MagnÃ©tisme"** (**First Memoir on Electricity and Magnetism**). In this work, he articulated the mathematical expression that we now know as Coulomb's Law.

****Coulomb's Law Equation:****

Here, ( F ) is the force between the charges, ( k ) is Coulomb's constant (**Is equal to ****1/4Ï€Îµ**), ( Q1) and ( Q2) are the magnitudes of the charges, and ( r ) is the distance between them , **(Îµ)** Is property of material which is default value 8.85 * 10-12 .

- Coulomb's Law was groundbreaking. It provided a quantitative measure of electric force, allowing scientists to predict and understand the behavior of charged objects. Coulomb's work earned him recognition, and his name is forever associated with this fundamental principle in electromagnetism.

**property of electric force**

- Electric force will always act along the line of joining (It means force applied by one object to another object always acts in line of joining of them).

- Nature Of electric force conservative (It means the charge the electric force doesn't change by Influence of external force) .

- Electric force always acts in pairs (It means electric force always lies with action and reactions) .

These properties align with when the charge is assumed to be at rest .

Coulomb's Law laid the foundation for further exploration of electricity and magnetism, contributing significantly to the development of the broader field of electromagnetism. It remains a cornerstone in physics and continues to be a fundamental tool in understanding electric interactions.

**Learn more excitement topics:**

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Q1:- Which charge particle experiences a long electric force ?

- 1000c
- 1c
- Equal
- Cannot say

So the right answer is 3 which is “equal” I know many of them think 1c will experience long electric force But they forget electric force always lies in pair, it means in action and reaction so when the **1000 coulomb** charge particle Force On **1 coulomb **charge particle then by reaction force** 1 coulomb** charge particle also force same amount of force to the **1000 coulomb** of charge particle. So they are equal and opposite .

**Effect of medium **

**Effect of medium**

So when we take charge particles +Q and -Q and dive into a medium like wise we take water then one charge particle will experience 2 forces ,first one electric force by another charge particle and second one is medium force which is in this case water.

So +Q charge particles will experience tow force first by -Q and second by buoyancy force which is water force so obviously we can see force will vary by medium to medium.

By this effect a one particular symbol becomes in the picture which is dielectric constant. It is nothing but the factor of force which reduces the Force between two charged particles .

**Q2. Coulomb's law correctly describes the electric force ?**

**Binds the electrons of an atom to its nucleus.**- Binds the proton and neutron in their nucleus of an atom.
- Binds the atoms together to form molecules.
- Bind the atom and molecules together to form a solid.

**Coulomb's law in vector form **

**Coulomb's law in vector form**

** Principle of superposition **

**Principle of superposition**

The force of attraction or repulsion between two charged particles is always free from surrounding charge particle there will be no effect on another charge particle .

It means when force between two charged particles is 5 Newton so there will be no change if any other charge particle comes near those charge particles.

Q3. **A charge Q is divided in two parts Q1 and Q2 and these charges are placed at a distance R. there will be maximum repulsion between them when** ?

1). Q1 = Q -q , Q2 = q

2). Q1 = 3Q/4 , Q2 = Q/4

3). Q1 = 2Q/3 , Q2 = Q/3

4). Q1 = Q2 = Q/2

**Equilibrium of charge particle**

**Equilibrium of charge particle**

Let suppose that we take to charge particles Q1 and Q2 and put them together and both charge particle experience same f electric force and now we take another charge particle q and put between Q1 and Q2, then q charge particle experience 0 force in this condition we will say that q is in equilibrium condition .

So the ratio of X1 and X2 is equal to the ratio of square root of Q1 and Q2. It means When we displace a small q charge particle from its equilibrium position it will try to retain its own equilibrium position again .Due to when we displace the unbalance force will occur between Q1 and q or Q2 and q so for balancing the force it will return it's on equilibrium position .

Q4. ** three charged particles +Q1 , q , + Q are placed respectively at distance 0 , d/2 and d from the origin, on the x-axis if the net force experienced by +Q1 placed at x = 0, is equal to zero then the value of q is ?**

**Let us see what is the equilibrium of a symmetric geometrical point charged system**

Let's try to find out what is the value of Q at the center for which system to be in a state of equilibrium .

for triangle shape :-

We have to find out the value of force on a Vertex .

So if we want Q is in equilibrium so you will have to applied a force which is **√3****F** at that vertex .

So for equilibrium condition Q should be -q/√3.

Q5. A **charge Q is placed at each of the opposite corners of the square. a charge q is placed at each of the other two corners . if the net electric force on a Q is zero then ****Q/q**** equals ?**

**Q6. Two charges each equal to small q1 are kept at (x = -a) and (x = a) on the x-axis A particle of mass M and charge ****q = -q/2**** is placed at the origin. if charge ****q**** not is given a small displacement ****(y << a)**** along the y axis , the net force acting on the particle is proportional to ? **

** Equilibrium of a suspended point charges system **

**Equilibrium of a suspended point charges system**

If we suspend two charged particles with the same polarity and fixed support then both charged particles repel to each other and particles go to the same distance .

**Conduction of charges by one body to another body :- **

**Conduction of charges by one body to another body :-**

When we take two Spears in which the first one is charged with the Q1 and second one is charged with Q2 when both Spears are connected by a wire then charge then high charges flow to low charge. so that they become equal, so after sometime we will see if we separate both by disconnecting wire we will find out that they become equal charges.

**Limitations of Coulomb's law :- **

**Limitations of Coulomb's law :-**

**Coulomb's law applicable only for the point charges not Applicable for the rod ,shape and cylinder and so on if it is applicable then****the charges must be concentrated around a small enough area not no longer area .**

**Coulomb's law is applicable only for stationary charge; it is not applicable while charge moves .**

**Learn more excitement topics:**

**learn more :**

- electric field and application (in easy way )
- electric force most important concepts with examples
- charge density (linear, area, volume with most helpful important examples )
- in-depth about charge with experiments
- what is electric flux: know every things about it with iits examples
- Application of gauss law