Find the potential due the dipole when the angle subtended by the two charges at the point P is perpendicular.

When considering an electric dipole, consisting of two charges of equal magnitude but opposite sign separated by a distance (d), the potential due to this dipole at a point in space can be derived from the principle of superposition. The electric potential (V) at any point due to a single point charge is given by the equation:

[V = frac{kQ}{r}]

where:

– (V) is the electric potential,

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

– (Q) is the charge,

– (r) is the distance from the charge to the point in space where the potential is being calculated.

For a dipole, the total potential at any point is the sum of the potentials due to each charge. At a point (P) that is perpendicular to the midpoint of the dipole, you would be considering a point along the axis that is perpendicular to the line joining the two charges (equatorial line). At this point, the contributions to the potential from each charge in the dipole are equal in magnitude but opposite in direction, effectively cancelling out. Consequently, if the observation point (P) is equidistant from both charges, the potential (V) at point (P) due to the dipole is theoretically zero.

However, for a general position perpendicular to the dipole but not equidistant to both charges (say,