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The electric potential (V) due to a dipole at a point in space is given by the equation:

[ V = frac{k cdot p cdot cos(theta)}{r^2} ]

where:

– (k) is the Coulomb’s constant ((8.987 times 10^9 , text{Nm}^2/text{C}^2)),

– (p) is the magnitude of the dipole moment ((q cdot d), where (q) is the charge magnitude and (d) is the separation distance between the charges),

– (theta) is the angle between the dipole moment vector and the line joining the point in space to the midpoint of the dipole,

– (r) is the distance from the midpoint of the dipole to the point in space where the electric potential is being calculated.

When the angle ((theta)) subtended by the two charges at the point (P) is perpendicular, i.e., (theta = 90^circ), (cos(90^circ) = 0). Therefore, the potential (V) at point (P) due to the dipole, when (theta = 90^circ), is:

[ V = frac{k cdot p cdot cos(90^circ)}{r^2} = frac{k cdot p cdot 0}{r^

a

Explanation: The potential due the dipole is given by, V = m cos θ/(4πεr

2

). When the

angle becomes perpendicular (θ = 90). The potential becomes zero since cos 90 will

become zero.