A water molecule is placed at a distance l from the line carrying linear charge density `lambda` . Find the maximum force exerted on the water molecule. The shape of water molecule and the partial charges on Hand O atoms are shown in figure

Explanation

The figure can be resolved as combination of 2 dipoles. Dipole moments of eachp = qd.

Here that dipole moment of system is
`P_("net")=2qdcostheta//2`
Now
`vec(F)=vec(P)_("net").(dvecepsilon)/(dx)`
For maximum force, the angle between `vecP_("net")` and `(dvecepsilon)/(dx) " is " 0^@`

`F_(max)=2qdcos.(theta)/(2)xxd/2xxd/(dx)((2klamda)/(x))`
or `F_(max)=2qdcos.(theta)/(2)xx2klamda(-1/(x^(2)))`
`=(-4Kqdlamdacostheta//2)/(x^(2))`
`|vec(F)_("max")|=(4Kqdlamdacostheta//2)/(x^(2))`
`|vec(F)_("max")|=(4Kqdlamdacostheta//2)/(l^(2))`