12. Consider Figure \( Q 12 \), three charges \( +Q,+Q \) and \( -2 Q \) of masses \( M, M \) and \( 2 M \) respectively are positioned at the vertex of an equilateral triangle with length \( L \).
Figure Q12
a) Find the coordinate of the centre of mass of the three charges; the origin is shown in the figure.
[5 marks]
b) The magnitude of the resultant electric field at the centre of mass is given by \( k \frac{Q}{4 \pi \epsilon L^{2}} \). Find the value of \( k \) and give your answer in four decimal places.
[10 marks]