For two charges 3C and -3C separated by 1cm and are located at distances 5cm and 7cm respectively from the point P, then the distance between their midpoint and the point P will be

Given two charges, (3C) and (-3C), separated by (1cm), and their distances from a point (P) being (5cm) and (7cm) respectively, we need to find the distance between their midpoint and the point (P).

First, let’s establish the positions of the charges and the point (P). Let’s assume the two charges are on a straight line, and (P) lies off this line. We are essentially working with a right-angled triangle, where the line segment connecting the charges acts as the base, and the lines connecting (P) to both charges act as the sides of the triangle. The midpoint of the charges will also lie on this base.

The charges are (1cm) apart. So, the midpoint of this (1cm) segment is (0.5cm) from each charge. This midpoint does not change the distances (P) has from the original positions of (5cm) and (7cm), as those lines would still emanate from the same points on the charges’ line, but we now consider the perpendicular from (P) to the midpoint.

Given the distances of (5cm) and (7cm), these seem to directly relate to the distances from (P) to each charge, not directly helpful in a simple calculation of the distance to the midpoint due to the geometry not being fully detailed. However, if we attempt to resolve this using the