Six equal point charges q0. each are placed at six corners of a regular hexagon of side 'a' .Find out required to take a point charge 'q' slowly : (i) From infinity to the centre of hexagon. (ii) From infinity to a point on the axis which is at a distance ' 3 a' from the centre of hex v, (iii) Does your answer to part (i) and (ii) depends on the path followed by the charge.

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Solution

Consider the charges at opposite sides of $0$ . They form dipole moment $P = 2 Q_{a}$
Electric field due to a dipole on its axis
$E = \frac{K_{p}}{x^{3}} = \frac{Q a}{2 π \in_{o} x^{3}}$
Net electric field $| E_{n e t} = 21 E |$
$= \frac{2 Q_{a}}{2 π \in_{o} x^{3}} = \frac{Q_{a}}{π \in_{o} x^{2}}$ .

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Consider the charges at opposite sides of 0. They form dipole moment P=2QaElectric field due to a dipole on its axisE=Kpx3=Qa2π∈ox3Net electric field |Enet=21E|=2Qa2π∈ox3=Qaπ∈ox2.