## How to calculate the magnitude of 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 proportional to the product of their masses and inversely proportional to the square of the distance between them,

\( F ~= ~k * \frac{Q1*Q2}{d^2} \)

Where F is the force of attraction of repulsion depending upon the charges,

K is the coulombs constant, for air it is 9×10^{9} N*m^{2}/C^{2
}Q1 and Q2 are the magnitudes of two charges

d is the distance between the two charges,

Let’s consider 3 charges Q_{A,} Q_{B }and Q_{C.}

We could get the net force acting on a charge by calculating the vector some 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,

\( \overrightarrow{F_1} ~=~ \mathop{\LARGE\mathrm \sum}_{j=1}^n F_{ij}\)

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

\( \overrightarrow{F_1} ~=~ \frac {1}{4 \pi \in} \left[ \frac {Q_A Q_B}{r^2_{AB}} \hat{r}_{AB} ~+~\frac {Q_A Q_C}{r^2_{AC}} \hat{r}_{AC} \right] \)

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.

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