Three point charges +q, -2q and +q are placed at the points (x=0, y=a, z=0), (x=0, y=0, z=0) and (x=a, y=0, z=0) respectively. The magnitude and direction of the electric dipole moment vector of this charge assembly are

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(2) √2 qa along the line joining the points (x=0, y=0, z=0) and (x=a, y=a, z=0). Split the -2q at the origin into two -q charges sitting on top of each other. Each pairs with one of the +q charges, giving two dipoles of the same size: p⃗₁=qa ĵ (from the origin toward (0,a,0)) p⃗₂=qa î (from the origin toward (a,0,0)) The dipole moment points from the negative charge to the positive one, so both arrows leave the origin. p⃗=p⃗₁+p⃗₂=qa(î+ĵ) |p⃗|=√(qa)²+(qa)²=√2 qa The resultant lies along the line from the origin to (a,a,0), at 45° between the two axes. The same result comes from p⃗=Σ qᵢr⃗ᵢ=q(0,a,0)-2q(0,0,0)+q(a,0,0)=qa(1,1,0), which is legitimate here because the assembly is neutral overall.

Three point charges +q, -2q and +q are placed at the points (x=0, y=a, z=0), (x=0, y=0, z=0) and (x=a, y=0, z=0) respectively. The magnitude and direction of the electric dipole moment vector of this charge assembly are

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