### Dipole and Charge Interaction**Diagram Overview:**The image illustrates a dipole consisting of a positive charge (+q) and a negative charge (-q). The dipole is depicted as aligned horizontally, with the following key points:- **Charge \( Q \):** Represented by a larger circle labeled \( Q \), positioned on the left.- **Distance \( r \):** The separation between charge \( Q \) and the negative end of the dipole (-q).- **Distance \( r + d \):** The separation between charge \( Q \) and the positive end of the dipole (+q), where \( d \) is the distance between the charges in the dipole itself.**Questions:****b) Formula for Total Force on the Dipole by Charge \( Q \):** Derive the mathematical expression for the net force experienced by the dipole due to the field of charge \( Q \).**c) Effect of Doubling Distance \( r \):** Consider the impact on the force magnitude if the distance \( r \) between charge \( Q \) and the dipole is doubled. Would the force magnitude increase, decrease, or remain unchanged? Analyze and explain the relationship. Lots of things that are electrically neutral overall have one side that's electrically negative and one side positive (a water molecule, for example). We call such things "electric dipoles," and we can model them as pairs of particles of charge \(+q\) and \(-q\) (where \(q\) is a positive number) separated by a distance \(d\). Usually, \(d\) is a very small distance. (For water it would be around \(10^{-11} \text{m}\), thinking of a few protons worth of charge on one end - about \(6 \times 10^{-19} \text{C}\) - and a few electrons worth at the other.) Furthermore, because of the magic of quantum mechanics, in many molecules it behaves more like a rigid rod than like a soft spring. So we can treat \(d\) as a fixed distance.**[Diagram Explanation]*The diagram shows two circles representing charges: a red circle labeled \(+q\) and a blue circle labeled \(-q\), connected by a line. This indicates the dipole separated by distance \(d\).Suppose you have a dipole that’s free to move in any way (including rotate – imagine it floating in space). And there’s an object with charge \(Q\) a distance \(r\) away. That distance \(r\) would be much larger than \(d\), the distance between the charges of the dipole, so we draw the dipole small.*[Second Diagram Explanation]*The second diagram shows a large circle representing charge \(Q\) and a smaller dipole (red and blue circles with a connecting line) at a distance \(r\).a) Consider the forces between the charge \(Q\) and the dipole. If the dipole is free to rotate:- Would the dipole end up attracted to the charge, repelled, or neither?- Would the charge \(Q\) be attracted, repelled, or neither to the dipole?- Do your answers depend on the sign of \(Q\)?

a. Considering that charge Q is positive, the negative part of the dipole would be attracted and…

Answered: a) Consider the forces between the…