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# Forces Between Multiple Charges

A charge is an inherent property of every atom, an atom is said to be charged if it has an unequal number of electrons and protons. An atom is said to be positively charged if it has less number of electrons than protons, and negatively charged if it has more electrons than protons.

The bodies get charged. Differently. The most common way of charging a body is to rub. If you rub a plastic comb with your hair, the comb attains electrons from the hair; now, if we get tiny pieces of paper close to the comb, it attracts the pieces like a magnet attracting iron fillings. This is because the electrons on the comb attract the positive charge on the paper. This is the force of charges in action.

## How to calculate the magnitude of the force between two charges?

We can find the force between any two charges by Coulomb’s law. Coulomb’s law states that two charged bodies will attract or repel each other with a force that is proportional to the product of their charges and inversely proportional to the square of the distance between them,

Let’s get an equation out of this,

$$\begin{array}{l} F ~= ~k * \frac{Q_1*Q_2}{d^2} \end{array}$$

Where F is the force of attraction or repulsion depending upon the charges,
k is the coulomb’s constant, for air, it is 9×109 N m2 C-2. Q1 and Q2 are the magnitudes of two charges
d is the distance between the two charges,

This is only applicable for two charged particles, how will we find a force on one charge due to multiple charges?

Let’s consider three charges Q1, Q2, and Q3.

We could get the net force acting on a charge by calculating the vector sum of all the forces acting on the charge, this is called the superposition theorem.

Considering the above example of 3 point charges Qa, Qb and Qc with a position vector of r1, r2 and r3. Then the force experienced by one charge due to the other charges is given by,

This can be written as,

$$\begin{array}{l} \overrightarrow{F_1} ~=~ \mathop{\LARGE\mathrm \sum}_{j=1}^n F_{ij}\end{array}$$
( where j ≠ i )

By applying this to our current situation of 3 point charges we will get,

$$\begin{array}{l} \overrightarrow{F_1} ~=~ \frac {1}{4 \pi \in} \left[ \frac {Q_A Q_B}{r^2_{AB}} \hat{r}_{AB} ~+~\frac {Q_A Q_C}{r^2_{AC}} \hat{r}_{AC} \right] \end{array}$$

This is a combination of the coulombs law and the superposition theorem, and any electro static force can be derived using coulombs law and the superposition theorem this way.

• The force acting on a charge is directly proportional to the magnitude of the charge and inversely proportional to the square of the distance between them.
• The force acting on a point charge due to multiple charges is given by the vector sum of all individual forces acting on the charges.

## Frequently Asked Questions – FAQs

### What is electrostatics?

Electrostatics is a branch of physics that deals with the phenomena and properties of stationary or slow-moving electric charges. Electrostatic phenomena arise from the forces that electric charges exert on each other and are described by Coulomb’s law.

### How does electrostatics work?

Electrostatic phenomena arise from the forces that electric charges exert on each other and are described by Coulomb’s law. Even though electrostatically induced forces seem to be relatively weak.

### Define current.

Current electricity is defined as the flow of electrons from one section of the circuit to another.

### What is DC current?

The current electricity whose direction remains the same is known as direct current. Direct current is defined by the constant flow of electrons from a region of high electron density to a region of low electron density. DC is used in many household appliances and applications that involve a battery.

### Define AC current.

The current electricity that is bidirectional and keeps changing the direction of the charge flow is known as alternating current.
Test Your Knowledge On Force Multiple Charges!

1. thrishank

Thanks