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To find the angle at which the potential due to a dipole is measured, given the distances from the charges, consider a dipole consisting of charges (+q) and (-q), separated by a distance (2a). The position where the potential is being measured forms a triangle with the line joining the charges. Given that the distances from the positive and negative charges are 12 cm and 11 cm, respectively, and the separation between the charges ((2a)) is 2 cm, we can find the angle using the law of cosines.

Let us denote:

– (r_+) as the distance from the positive charge ((12 cm)),

– (r_-) as the distance from the negative charge ((11 cm)),

– (d = 2 cm) as the distance between the charges,

– (theta) as the angle the position vector (from the negative to the positive charge) makes with the perpendicular bisector of the dipole.

Using the law of cosines on the triangle formed by the position of measurement and the two charges, we have:

[r_+^2 = r_-^2 + d^2 – 2 cdot r_- cdot d cdot cos(theta)]

Substituting values:

[12^2 = 11^2 + 2^2 – 2 cdot 11 cdot 2 cdot cos(theta)]

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