Question

A small electric dipole having dipole moment
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` vec p` is placed along x-axis as shown in the figure . A semi-infinite uniformly charged di-electric thin rod is placed along `x` axis , with one end coinciding with origin . If linear charge density of rod is `+ lambda` and distance of dipole from rod is `a` then calculate the electric force acting on dipole .

Answer 1

Correct Answer - ` (- P lambda)/( 4 pi varepsilon_0 a^2)`.
Field at `P` due to elemental length is
`dE = (K lambdadx)/(x^2)`
`E = int dE = K lambda int _a^(infty) = (K lambda)/a = 1/(4 pi in_0) (lqambda)/a`
Potential energy of dipole `U =- Pe cos theta`
`U = - ( p lambda) /( 4 pi in_0 a)`
`F= - (dU)/(da) rArr F= ( lambda )/(4pi in_0 a^2)`.