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An electric dipole is placed perpendicular to an infinite line of charge at some distance as shown in figure . Identify the correct statement

$(a)\;The\;dipole\;is\;attracted\;towards\;charge\qquad(b)\;It\;is\;repelled\;away\;from\;charge\qquad(c)\;It\;does\;not\;experience\;a\;force\qquad(d)\;None\;of\;these$

Answer : (a) The dipole is attracted towards charge
Explanation :
$F_{-q}=(E_{-q})(-q)\;\hat{i}$
$F_{-q}=-\large\frac{\lambda\;q}{2 \pi \in_{0}\;(x-d)}\;\hat{i}$
$F_{+q}=\large\frac{\lambda\;q}{2 \pi \in_{0}\;(x+d)}\;\hat{i}$
$F_{net}=F_{-q}+F_{q}=\large\frac{\lambda\;q}{2 \pi \in_{0}}\;\large\frac{(-(x+d)+(x-d))}{(x^2-d^2)}$
$F_{net}=-\large\frac{2\;\lambda\;q\;d}{2\;\pi\;\in_{0} \;x^2}\; \hat{i}$
$F_{net}=-\large\frac{\lambda\;\overrightarrow{P}}{2\;\pi\;\in_{0}\;x^2}$
So , dipole will be attracted by the line charge .
edited Aug 22, 2014 by meena.p