Six charges, three positive and three negative of equal magnitude are to be placed at the vertices of a regular hexagon, such that the electric field, at the centre O is double the electric field when only positive charge of same magnitude is placed at R. Which of the following arrangements of charges is possible for P, Q, R, S, T and U respectively?

+, -, +, -, -, +

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+, -, +, -, +, -

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+, +, -, +, -, -

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-, +, +, -, +, -

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Solution

The correct option is D $-, +, +, -, +, -$
To get two times electric than earlier place -ve charge on U.Electric field due to U and R is 2 times than only due to R.Now place 2 positive and 2 negative to cancel each other. Place +ve at P and S and -ve at Q and T or -ve at P as S and =ve at Q and T.So possible arrangement is either +,-,+,+,-,-or -,+,+,-,+,-

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