The smilling face of Fig, consists of three parts ,
(i) a thin rod of charge `-3.0 muC` that forms a full circle of radius 6.0 cm.
(ii) a thin rod of charge `2.0 muC` that forms a circular are of radius 4.0 cm, subtending an angle of `90^(@)` about the centre of full circle, and
(iii) and electric diipole with dipole moment `= 1.28xx10^(-21)` Cm perpendicular to a radial line as shown in Fig. What is the net electric potentail as the centre ?

Explanation

Here, `q_(1) = -3.0 muC, r_(1) = 6.0 cm`
`V_(1) = (q_(1))/(4pi in_(0) r_(1)) = (k-(-3.0))/(6.0) = - (k)/(2) muC//cm`,
where `k = (1)/(4pi in_(0))`
Again, `q_(2) = + 2 muC, r_(2) = 4.0 cm`
`V_(2) = (q_(2))/(4pi in_(0) r^(2)) = (k(+2.0))/(4.0)= (k)/(2) muC//cm`,
For the dipole, `theta = 90^(@)`
Potential due to dipole at the center
`V_(3) = (p cos theta)/(4pi in_(0) r^(2)) = (p cos 90^(@))/(4pi in_(0) r^(2)) = 0`
`:.` Net electric potential at the center
`V = V_(1) + V_(2) + V_(3) = (k)/(2) (k)/(0) + 0 = ` zero.