Two point charges `q_(A) =3 muC` and `q_(B) = -3 muC` are located 20 cm apart in vacuum.
(a) What is the electric field at the midpoint O of the line AB joining the two charges ?
(b) If a negative test charge of magnitude `1.5 xx 10^(-9)` C is placed at this point, what is the force experienced by the test charge ?

Explanation

(a) Electrical field at C due to `q_(A)` is,
`vecE_(CA) = (k|q_(A)|)/r_(CA)^(2) hati` (From A to C)………..(1)
Electric field at C due to `q_(B)` is,
`vecE_(CB) = (k|q_(B)|)/r_(CB)^(2).hati` (From C to B)
`therefore vecE_(CB) = vecE_(CA)`
`(therefore |q_(A)| = |q_(B)|)` and `r_(CA) = r_(CB)`)
Now resultant electric field at C would be,
`vecE_(C) = vecE_(CA) + vecE_(CB)`
`=2vecE_(CA)` (`therefore` From equation (2))
`=2(kq_(A))/(r_(CA)^(2)) hati`
`therefore vecE_(C) = 5.4 xx 10^(6) N//C hati` (From `q_(A)` to `q_(B)`)
(b) Electric force exerted on `q_( C)`, placed at C (midpoint of `bar(AB)`)
`vecF_(e) = q_( C) vec(E)c`
`=(1.5 xx 10^(-9))(5.4 xx 10^(6))hati`
`therefore vecF_(e) = 8.1 xx 10^(-3) Nhati` (From `q_(A)` to `q_(B)`)