Six charges of equal magnitude, 3 positive and 3 negative, are to be placed on PQRSTU corners of a regular hexagon, such that the field at the centre is double that of what it would have been if only one +ve charge is placed at R. Which of the following arrangement of charge is possible for P, Q, R, S, T and U respectively [2004]

Question

Smart Achievers · Accepted Answer

(3)

Electric field, $| \vec{E} |$ $= \frac{K q}{r^{2}}$

Electric field due to P on O is cancelled by the electric field due to S on O.

Similarly, electric field due to Q on O is cancelled by the electric field due to T on O.

The electric field due to R on O is in the same direction as that of U on O.

Hence the net electric field $\vec{E} + \vec{E} = 2 \vec{E} .$

Solution

1 +, +, +, −, −, −

2 −, +, +, +, −, −

3 −, +, +, −, +, −

4 +, −, +, −, +, −

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