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

Figure
`E=1/(4piepsilon_0) Q/r^2`
`E_A=E_B=2700xx10^3`
`=2.7xx10^6` N/C
Resultant field
`E_R=E_A+E_B =5.4xx10^6` N/C along AB
Force F=Eq=`8.1xx10^(-3)` N along BA
Given , `q_A=3xx10^(-6) C, q_B=-3xx10^(-6)C` , r=0.20 m
(a) Electric field at the mid-point .O.

`E=1/(4piepsilon_0).Q/r^2`
`E=(9xx10^9xxQ)/r^2 Vm^(-1)`
Hence `E_A=E_B=(9xx10^9xx3xx10^(-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_B`
`=5.4xx10^(6) Vm^(-1)` along OB
(b)Net force on `-1.5xx10^(-9)` C placed at .O.
`F=q_0E_0`
i.e., `F=-1.5xx10^(-9)xx5.4xx10^9` N
`=8.10xx10^(-3)` N in the direction along OA.