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Offline Centres

Q.

Six point charges are kept at the vertices of a regular hexagon of side L and centre O, as shown in the figure. Given that $K = \frac{1}{4 {πε}_{0}} \frac{q}{L^{2}}$ . Which of the following statement (s) is (are) correct?

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a

The potential at O is zero

b

The potential at all points on the line PR is same

c

The potential at all points on the line ST is same

d

The electric field at O is 6K along OD

answer is A, B, C.

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Detailed Solution

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$E_{2} = E_{3} = \frac{2 Kq}{L^{2}} \Rightarrow E_{1} = \frac{4 Kq}{L^{2}} E_{all} = {\vec{E}}_{1} + {\vec{E}}_{2} + {\vec{E}}_{3} = \frac{6 kq}{L^{2}} = 6 \times \frac{q}{4 {πε}_{0} L^{2}} = 6 K (AlongOD) V at O = 0$
$V_{at}$ line PR is zero because this line is the equatorial axis for the three dipoles.

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