Two tiny spheres carrying charges `1.5muC` and `2.5muC` are located 30 cm apart. Find the potential and electric field :
(a) at the mid-point of the line joining the two charges and
(b) at a point 10 cm from this midpoint in a plane normal to the line and passing through the mid-point.

Explanation

Here `q_1=1.5,C=1.5xx10^-6C`,
`q_2=2.5muC=2.5xx10^-6C`
Distance between the two spheres = 30 cm =0.3cm.

(a) `V=?,E=?` from the mid point O.
`r_1=r_2=(0.3)/(2)=0.15m`'
`V=(1)/(4piepsi_0)[(q_1)/(r_1)+(q_2)/(r_2)]=2.4xx10^5"Volt"`.
(ii) Electric field at `O_2`.
`E=E_(2)-E_(1)=(1)/(4piepsi_0r^2)(q_2-q_1)`
`=(9xx10^9(2.5xx10^-6-1.5xx10^6))/((0.15)^2)`
`=4.0xx10^5Vm^-1`.
Clearly , `vec(E)` is towards `q_1`.
(b) Let P be the point in a plane normal to the line passing through the mid point ,
where `OP=10cm=0.1m`
From figure ,
Now `PA=PB`
`=sqrt((0.15)^2+(0.1)^2)m=0.18m`