Two dipoles with dipole moments -5az nC-m and 9az nC-m are located at points (0, 0, -2) and (0, 0, 3), respectively. What is the potential at the origin?

To find the electric potential at the origin due to the two dipoles.

Where p1 and p2 are the dipole moments, r1 and r2 are the distance from the dipoles to the point of interest.

P1 = (0,0,-2), -5a_z nC-m

p2 = (0,0,3), 9a_z nC-m

P0 = (0,0,0) (V = V₁ + V₂)

Potential (V) = \(\frac{KP\cdot a_r}{r^2} \)

K = \(\frac{1}{4\pi\varepsilon_0}= 9\times10^9\)

\(V_1 = \frac{9\times 10^9 \times(-5a_z\times10^-9)\cdot a_z}{2^2}\)

\(V_1 = -\frac{45}{4}\)

\(V_1 = \frac{9\times 10^9 \times(9a_z\times10^-9)\cdot a_z}{3^2}\)

V₂ = -9

V = V₁ + V₂ = \(-\frac{45}{4}-9 = -20.25V\)

Here, option 3 is correct.