**Forces Between Multiple Charges – Superposition Theorem**

According to the parallelogram law of addition. Experimentally it is verified that force on any charge due to a number of other charges is the vector sum of all the forces on that charge due to the other charges, taken one at a time. The individual forces are unaffected due to the presence of other charges. This is termed as the *principle of superposition*.

*Fig.2 A system of (a) three charges (b) multiple charges.*

To better understand the concept, consider a system of three charges q_{1}, q_{2}, q_{3}, as shown in Fig.2. The force on one charge, say *q*1, due to two other charges *q*2, *q*3 can, therefore, be obtained by performing a vector addition of the forces due to each one of these charges.

Thus the total F_{1} on q_{1} due to the two charges q_{2} and q_{3} is given as

The above calculation of force can be generalized to a system of charges more than three, as shown in fig.1(b)

The **principle of superposition** says that in a system of charges *q*_{1}, *q*_{2}, *…, q _{n}, *the force on

*q*

_{1}due to

*q*

_{2}is the same as given by Coulomb’s law, i.e., it is unaffected by the presence of the other charges

*q*

_{3},

*q*

_{4},

*…, q*

_{n}. The total force

**F**

_{1}on the charge

*q*1, due to all other charges, is then given by the vector sum of the forces

**F**,

_{12}**F**

_{13},…,

**F**

_{1n}:

The vector sum is obtained as usual by the parallelogram law of addition of vectors. All of the electrostatics is basically a consequence of Coulomb’s law and the superposition principle.