Electric an the due to the system of point charges : Suppose a number of point charges are distributed in space. To find the electric field at some point P due to this collection of point charges, superposition principle is used. The electric field at an arbitrary point due to a collection of point charges is simply equal to the vector sum of the electric fields created by the individual point charges. The is called superposition of electric fields.
Consider a collection of point charges `q_(1) , q_(2). q_(3), ........, q_(n)` located at various points in space. the total electric field at some point P due to all these n charges is given by
`vecE_("tot") = vec(E_(1)) + vec(E_(2)) + vec(E_(3)) + ..... + vec(E_(n))" "`....(1)
`vec(E_("tot")) = (1)/(4 pi epsilon_(0)) { (q_(1))/(q_(1)^(2)p) hat(r)_(1p) + (q_(2))/(q_(2p)^(2)) hat(r)_(2p) + (q_(3))/(q_(3p)^(2)) hat(r)_(3p) + ...... + (q_(n))/(q_(nP)^(2)) hat(r)_(nP) }" "`(2)
Here `r_(1p), r_(2p), r_(3p), ..... r_(nP)` are the distance of the charges `q_(1),q_(2),q_(3),........ q_(n)` from the point P respectively. Also `hat(r)_(1P) + hat(r)_(2p) + hat(r)_(3p)+ ..... + hat(r)_(np)` are the
corresponding unit vectors directed from `q_(1),q_(2),q_(3)`.... `q_(n) ` to P.
Equation (2) can be re-written as.
`vec(E_("tot")) = (1)/(4 pi epsilon_(0)) sum_(i l)^(n)((q_(1))/(q_("ip")^(2)) hat(r)_(ip))" "`.....(3)
For example in figure, the resultant electric field due to three point charges `q_(1), q_(2), q_(3)` at point P is shown. Note that the relative lengths of the electric field vectors for the charges depend on relative distances of the charges to the point P.
