1.

Six charges are placed at the vertices of a regular hexagon as shown in the figure. The electric field on the line passing through point O and perpendicular to the plane of the figure at a distance of x (gt gt a) from O is

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SOLUTION :This is basically a problem of finding the electric field due to three dipoles. The dipole moment of each dipole is P = Q(2a) Electric field due to each dipole will be `E= (KP)/(X^(3))`

The DIRECTION of electric field due to each dipole is as shown below:
`E_("net") = E + 2E cos 60^(@)= 2E`
`=2 ((1)/(4pi epsi_(0))) (2Qa)/(x^(3))= (QA)/(pi epsi_(0)x^(3))`


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