Question: Q. 8. (i) An electric dipole is kept first to the left and then to the right of a negatively charged infinite plane sheet having a uniform surface charge density. The arrows $p_{1}$ and $p_{2}$ show the directions of its electric dipole moments in the two cases.
Identify for each case, whether the dipole is in stable or unstable equilibrium. Justify each answer.
(ii) Next, the dipole is kept in a similar way (as shown), near an infinitely long straight wire having uniform negative linear charge density.
Will the dipole be in equilibrium at these two positions? Justify your answer. A [SQP 2018-19]
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Solution:
Ans. (i) $p_{1}$ : stable equilibrium
$p_{2}$ : unstable equilibrium
The electric field, on either side is directed towards the negatively charged sheet and its magnitude is independent of the distance of the field point from the sheet. For position $p_{1}$, dipole moment and electric field are parallel. For position $p_{2}$, they are anti parallel. $1 / 2+1 / 2$
(ii) The dipole will not be in equilibrium in any of the two positions.
The electric field due to an infinite straight charged wire is non-uniform ( $\mathrm{E} \alpha 1 / r$ ).
$1 / 2$ Hence, there will be a net non-zero force on the dipole in each case.
[CBSE Marking Scheme, 2018-19]
