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Six point charges are kept at the vertic...

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=(1)/(4piepsilon_0)(q)/(L^2)`, which of the following statements(s) is (are) correct?

A

(a) The electric field at O is 6K along OD

B

(b) The potential at O is zero

C

(c) The potential at all points on the line PR is same

D

(d) The potential at all points on the line ST is same

Text Solution

Verified by Experts

The correct Answer is:
A, B, C


Here `(|vecE_A|)/(2)=|vecE_B|=|vecE_C|=(|vecE_D|)/(2)=|vecE_E|=|vecE_F|=K`
`:.` `E_O=E_A+E_D+(E_F+E_C)cos 60^@+(E_B+E_C)cos 60^@`
`=2K+2K+(K+K)xx1/2+(K+K)xx1/2=6K`
The electric potential at O is
`V_O=(1)/(4piepsilon_0L)[2q+q+q-q-q-2q]=0`
PR is perpendicular bisector (the equatorial line) for the electric dipoles AB, FE and BC. Therefore the electric potential will be zero at any point on PR.
At any point ST, the electric field will be directed from S to T. The potential decreases along the electric field line.
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