Forces Between Multiple Charges

Consider a system of n stationary charges q₁, q₂, q₃, ..., qn in vacuum. 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.

Consider a system of three charges q₁, q₂ and q_3, as shown in Fig. The force on one charge, say q1, due to two other charges q2, q3 can therefore be obtained by performing a vector addition of the forces due to each one of these charges. Thus, if the force on q₁ due to q₂ is denoted by F12, F12 is given by

 In the same way, the force on q₁ due to q₃, denoted by F13, is given by

  This again is the Coulomb force on q₁ due to q_3, even though other charge q2 is present.

Thus the total force F1 on q₁ due to the two charges q₂ and q₃ is given as

The above calculation of force can be generalized to a system of charges more than three, as shown in below Fig.

The principle of superposition says that in a system of charges q1,q2, ..., qn, the force on q1 due to q2 is the same as given by Coulomb’s law, i.e., it is unaffected by the presence of the other charges q3, q4, ..., qn.

The total force F1 on the charge q1, due to all other charges, is then given by the vector sum of the forces F12, F13, ..., F1n:

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

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Some of these questions which may be asked in your Board Examination 2012-2013

Q1: When a plastic comb is passed through dry hair, what type of charge is acquire by comb?

Q2: Does motion of a body affect its charge?

Q3: What is the origin of frictional forces?

Answer these questions in comment box and help your friends