Determine the electric dipole moment of the system of three charges, placed on the vertices of an equilateral triangle, as shown in the figure [charge -2q at the apex, charge +q at each of the two base vertices, side of the triangle =l, the base lying along the x-axis and the y-axis drawn upward th…

Question

Determine the electric dipole moment of the system of three charges, placed on the vertices of an equilateral triangle, as shown in the figure [charge -2q at the apex, charge +q at each of the two base vertices, side of the triangle =l, the base lying along the x-axis and the y-axis drawn upward through the left-hand +q]

Accepted Answer

(4) -√3 ql ̂j. Take the base vertices at (0,0) and (l,0), each carrying +q, and the apex at (l/2,(√3 l)/2) carrying -2q. The system is neutral, so ⃗p=Σ qᵢ⃗rᵢ may be computed about any origin. x-component: q(0)+q(l)+(-2q)l/2=ql-ql=0. y-component: q(0)+q(0)+(-2q)(√3 l)/2=-√3 ql. ⃗p=-√3 ql ̂j, i.e. of magnitude √3 ql pointing from the -2q apex down towards the base, as a dipole moment must point from negative to positive charge.

Step-by-step solution

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