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 arc unaffected due to the presence of other charges. This is termed as the principle of superposition.
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 Jaw, i.e., it is unaffected by the presence of the other charges `q_3, q_4, .......q_n.` The total force `vecF_1` on the charge `q_1`, due to all other charges, is then given by the vector sum of the forces `vecF_(12) , vecF_(13) , ... , vecF_(1n) : `
`vecF_1 = vecF_(12) + vecF_(13) +......+vecF_(1n)`
`= 1/(4pi epsilon_0)[(q_1q_2)/r_(12)^2 hat(r_(12)) + (q_1q_3)/r_(13)^2 hat(r_(13)) +........+(q_1q_n)/r_(1n)^2 hat(r_(1n))]`
`= q_1/(4pi epsilon_0) sum_(i=2)^n q_i/r_(1i)^2 hat(r_(1i))`
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.
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 arc unaffected due to the presence of other charges. This is termed as the principle of superposition.
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 Jaw, i.e., it is unaffected by the presence of the other charges `q_3, q_4, .......q_n.` The total force `vecF_1` on the charge `q_1`, due to all other charges, is then given by the vector sum of the forces `vecF_(12) , vecF_(13) , ... , vecF_(1n) : `
`vecF_1 = vecF_(12) + vecF_(13) +......+vecF_(1n)`
`= 1/(4pi epsilon_0)[(q_1q_2)/r_(12)^2 hat(r_(12)) + (q_1q_3)/r_(13)^2 hat(r_(13)) +........+(q_1q_n)/r_(1n)^2 hat(r_(1n))]`
`= q_1/(4pi epsilon_0) sum_(i=2)^n q_i/r_(1i)^2 hat(r_(1i))`
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.