The point charges +q , -q , -q , +q , +Q and -q are placed at the vertices of a regular hexagon ABCDEF as shown in the figure. The electric field at the centre of the hexagon 'O' due to the five charges at A, B, C, D and F is thrice the electric field at centre 'O' due to charge +Q at E alone. The value of Q is

Step-by-step solution

Let the distance from each vertex of the regular hexagon to its center O be r . The electric field at the center O due to a point charge q at a distance r has a magnitude E = 1 4 ₀ q r^2 . In the regular hexagon ABCDEF, the pairs of diametrically opposite vertices are (A, D), (B, E), and (C, F). The charges at A and D are both +q . The electric fields produced by these two charges at the center O are equal in magnitude and opposite in direction, thus they cancel each other out. The charges at C and F are both -q .