The point charges +q,-q,-q,+q,+Q and -q are placed at the vertices of a regular hexagon ABCDEF as shown in figure. The electric field at the centre of 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

Electric field at ' O ' due to charge ' Q ' is given by, E= k Q r^2 Electric field at ' O ' due to charges +q at A and D are equal and opposite and hence they will cancel each other. Similarly electric field at ' O ' due to charges -q at F and C will also cancel each other. Electric field at ' O ' due to charge -q at B is given by, E^ = k q r^2 Now, E ^ =3 E kq r ^2 = 3 kQ r ^2 Q = q 3