Obtain the equation of electric field at a point by system of 'n' point charges.

Explanation

As shown in figure, `q_(1), q_(2),`………. `q_(n)` charges are at `vecr_(1), vecr_(2)`,………..`,vecr_(n)` from origin O.

Electric field at P of position vector `vecr_(1P)`
`vecE_(1) = 1/(4pi epsilon_(0)).q_(1)/q_(2)hatr_(1P)`
where `vecr_(1P)` is unit vector in direction from `q_1` to E Electric field at P of position vector `vecr_(2P)`
`E_(2) = 1/(4pi epsilon_(0)).q_(2)/r_(2P)^(2) hatr_(2P)`
Similarly electric fields by `q_(3), q_(4)`,.........`q_(n)` at P are `vecE_(3), vecE_(4)`,..........`vecE_(n)` can be obtained and resultant field `vecE` can be obtained.
`vecE(vecr) = vecE_(1)(vecr) + vecE_(2) (vecr) +`........`vecE_(n)(vecr)`
`vecE(vecr) = 1/(4pi epsilon) sum^(n) q_(1)/q_(2)hatr_(iP)`, where i=1,2,...........,n
`vecE` is vector quantity and it varies by point to point in space and it is decided by positions of source charges