Two point charges `q_(A)=3muC` and `q_(B)=-3muC` are located 0.2 m apart in vacuum.
a. What is the electric field at the mid point O of the line AB joining the two charges?
b. If a negative test charge of magnitude `1.5xx10^(-9)C` is placed at this point, what is the force experienced by the test charge?

Explanation

Given `q_(A)=3 xx 10^(-6) C, q_(8)=-3 xx 10^(-6) C, r= 0.2 m`
(a) Electric field at the midpoint '0'

wkt `E=(9xx10^(-9))/(r^(2)) vm^(-1)`
Hence `E_(A)=E_(B)=(9xx10^(9)xx3xx10^(-6))/(0.10)^(2)`
i.e `E_(A)=E_(B)=(27xx10^(3))/(10^(-2))=27xx10^(5) Vm^(-1)`
The direction along AB or OB
`therefore` Net electric field at `=E_(A)+E_(n)`
`=5.4xx10^(6) Vm^(-1)` along OB
(b) Net force on `1.5 xx10^(-9)` C placed at '0'
`F=q_(0)E_(0)`
i.e `F=-1.5 xx10^(-9)xx5.4 xx10^(6) N`
`=8xx10^(-3)` N in the direction along OA