An electric dipole consists of charges `pm 2.0 xx 10^(8) C` separated by a distance of `2.0 xx 10^(-3)` m. It is placed near a long line charge of linear charge density `4.0 xx 10^(-4) C m^(-1)` as shown in figure (30-W4), Such that the negative charge is at a distance of `2.0 cm from the line charge. Find the force acting on the dipole.

Explanation

Here, `q = +- 2.0xx10^(-8) C`
`2a = 2mm = 2xx10^(-3)m`
`lambda = 4.0xx10^(-4) C//m`

Distanc eof `-q` charge from line charge,
`r_(1) = 2cm = 0.2 m`
Eelectric field at location of `-q` due to line charge.
`E_(1) = (lambda)/(2pi in_(0) r_(1)) = (2xx9xx10^(9)xx4xx10^(-4))/(0.02)`
`= 3.6xx10^(8) N//C`
Force on `-q` due to line charge
`F_(1) = qE_(1) = 2xx10^(-8)xx3.6xx10^(8) = 7.2 N`
The direction of `F_(1)` is towards the line charge. Electric field at the location of `+q` due to the line chage,
`E_(2) = (lambda)/(2pi in_(0) r_(2)) = (2xx9xx10^(9)xx4xx10^(-4))/((0.002 + 0.002))`
Force on `+q` due to line charge,
`F_(2) = qE_(2) = 2xx10^(-8)xx3.27xx10^(8) = 6.54 N`
The direction of `F_(2)` is away from the line charge.
`:.` Net force on electric dipole `= F_(1) - F_(2)`
`= 7.2-6.54 = 0.66N`
The net force is directed towards the line charge.