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To find the distance between the midpoint of the two charges and the point P, we first understand that the charges are separated by 1 cm, implying they lie on a straight line with each other. The charges are 3C and -3C, but this information is not directly relevant for calculating the distance to the midpoint; it is more relevant in electrostatic force or field calculations.

Given distances from P:

– The distance from P to the 3C charge is 5 cm.

– The distance from P to the -3C charge is 7 cm.

Since the charges are 1 cm apart, if we represent this linearly, we have two scenarios depending on the order of the charges regarding point P:

### 1. P closer to 3C charge:

– P —– 5cm —– 3C —– 1cm —– -3C —– 7cm (not possible based on the given distances; this arrangement would mean P is closer to -3C)

### 2. P closer to -3C charge, which fits the given distances:

– 3C —– 1cm —– -3C —– 5cm —– P —– 7cm (also not logical based on initial direct reading but helps picturing the scenario opposite to the initial assumptions)

### Correct logical arrangement:

– Considering the midpoint between charges is directly in the middle of the 1 cm gap, making the distances from P to each charge conceptually misunderstood in the depiction.

a

Explanation: For a distant point P, the R1 and R2 will approximately be equal.

R1 = R2 = r, where r is the distance between P and the midpoint of the two charges.

Thus they are in geometric progression, R1R2=r2

Now, r2 = 5 x 7 = 35. We get r = 5.91cm