Two point charges `q_A= 3muC and q_(B) = -3muC` 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. `E=E_(1)+E_(2)`
`E_(t)=(9 xx 10^(9) q_(A))/((AO)^(2)) =(9 xx 10^(9) xx 3 xx 10^(-5))/((10 xx 10^(-2))^(2)) =27 xx 10^(5) "N/C along OB"`
`E_(2)=(9 xx 10^(9) q_(B))/((BO)^(2))=(9 xx 10^(9) xx 3 xx 10^(-6))/((10 xx 10^(-2))^(2)) =27 xx 10^(5)" N/C along OA"`
`E=E_(1)+E_(2) =54 xx 10^(5) NC^(-1)" along OB"`
b. `F_(1)=9 xx 10^(9) (q_(A)q)/((OA)^(2)) =(9 xx 10^(9) xx 3xx 10^(-6) xx 1.5 xx 10^(-9))/((10 xx 10^(-2))^(2)) =40.5 xx 10^(-4)N`
`F_(2)=(9 xx 10^(9) xx 3 xx 10^(-6) xx 1.5 xx 10^(-9))/((10 xx 10^(-2))^(2)) =40.5 xx 10^(-6)N`
`F=F_(1)+F_(2)=81 xx 10^(-4)" N along OA"`