The theorem states that for n colinear charges, the sum Σqᵢcosθᵢ remains constant when θ is measured in the same sense. The proof can be established geometrically by setting up the charges along a line and analyzing the angular relationships. Alternatively, the theorem can be proven more elegantly using complex analysis techniques, which simplify the trigonometric components into complex exponential forms. This approach leverages the properties of complex numbers to demonstrate the constancy of the sum definitively.
Physics students, electrical engineers, and mathematicians interested in electrostatics, vector analysis, and complex analysis applications in physics will benefit from this discussion.