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Question: an electric field can induce an electric dipole in a...

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An electric field can induce an electric dipole in a neutral molecule (or atom) by pushing the positive and negative charges inside the molecule in opposite directions. The dipole moment of the induced dipole is directly proportional to the electric field at the molecule. That is, p⃗ =αE⃗ , where  p⃗   is the induced dipole moment, α is called the polarizability of the molecule, and  E⃗  is the electric field at the molecule. A stronger electric field at the molecule results in a more polarized molecule and causes a larger dipole moment p⃗ . A molecule with a larger polarizability, α, will be more polarized when subjected to the same electric field.

A.

An ion with positive charge q is a distance r from a neutral, nonpolar molecule.

The Introduction to the problem states, "The dipole moment of the induced dipole is directly proportional to the electric field at the molecule."

What is the electric field at the molecule?

Express your answer in terms of the variables q, r and appropriate constants like ϵ0.

B.

The molecule has a polarizability α. Find an expression for the dipole moment ( p⃗  ) induced in the molecule. Assess and justify the direction of the dipole moment vector you draw.

Express your answer in terms of the variables q, r, α and appropriate constants.

C.

Now that the molecule has a dipole moment, there is a net electric force acting on the molecule.

Create a model for the molecule's dipole moment. Explain why there is a net electric force on the molecule and what direction the net force points. Assume that the distance r is larger than the charge separation within the dipole.

D.

Find an expression for the force the electric field from the ion exerts on the molecule  F⃗ iononmolecule . Assume that the distance r is much larger than the charge separation within the dipole.  

Express your answer in terms of the variables q, r, α and appropriate constants. Don't forget that since force is a vector your answer must include the direction of the force.

E.

Since the molecule now has a dipole moment, it creates an electric field in all the space around it.

What is the direction of this electric field at the ion's position? Assess and justify the direction of the electric field vector you draw.

F.

Find an expression for the force the electric field from the molecule exerts on the ion F⃗ moleculeonion.

Express your answer in terms of the variables q, r, α and appropriate constants. Don't forget that since force is a vector your answer must include the direction of the force.

G.

Explore the forces:

Do the ion and molecule attract, repel, or neither attract nor repel?
If the ion's charge is doubled, how do the forces change?
If the distance between the ion and the molecule is doubled, how do the forces change?
If the molecule's polarizability is doubled, how do the forces change?
If the ion has a negative charge, how do the forces change?

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