# Why is the Electric Field of a Polarized Atom Different in Textbooks?

• Tony Hau
In summary, the conversation revolves around the calculation of the electric field inside a uniformly charged sphere. While the solution provided in the textbook is complicated, one of the speakers suggests using Coulomb's law to simplify the calculation. However, there is confusion about whether the electron cloud can be treated as a point charge or not.
Tony Hau
Homework Statement
A primitive model for an atom consists of point molecules ##(+q)## surrounded by a uniformly charged spherical cloud ##(-q)## of radius ##a## (Fig.1). Calculate the atmoic polarizability of such an atom.
Relevant Equations
##E_{dip}(r,\theta) = \frac {p}{4 \pi \epsilon_o r^{3}}(2cos(\theta)\hat {\mathbf r} + sin(\theta) \hat {\mathbf \theta}) ##
The question is like this:

The solution is like this:

However, according to the equation for ##E_{dip}## , what I think is that it should be: $$E=\frac {1}{4 \pi \epsilon_o} \frac {qd}{d^3} \hat {\mathbf z}$$, where I take the centre of the sphere in figure 2 as the centre of the coordinate, and positive z-axis towards right.

Actually it doesn't have to be that complicated. The electric field experienced by the positive charge on the left in figure 2 can be simply calculated by the Coulomb's law ##E=\frac{1}{4 \pi \epsilon_o}\frac{-q}{r^2}##. Anyway, I don't know why the textbook gives something different.

Last edited:
Tony Hau said:
The electric field experienced by the positive charge on the left in figure 2 can be simply calculated by the Coulomb's law ##E=\frac{1}{4 \pi \epsilon_o}\frac{-q}{r^2}##.

Really? It is a uniformly charged sphere and we are calculating the electric field inside the sphere!

Abhishek11235 said:
Really? It is a uniformly charged sphere and we are calculating the electric field inside the sphere!
I suppose we can treat the electron cloud as a point charge, just like what we do for centre of mass? If that's not the case, why would the author draw two points inside the sphere?

## 1. What is an electric field?

An electric field is a physical quantity that describes the influence that an electric charge has on other charges in its vicinity. It is a vector field, meaning it has both magnitude and direction.

## 2. How is an electric field created by a polarized atom?

When an atom is polarized, its positive and negative charges are separated, creating a dipole moment. This dipole moment creates an electric field around the atom.

## 3. How does the strength of the electric field depend on the polarization of the atom?

The strength of the electric field is directly proportional to the polarization of the atom. The more polarized the atom is, the stronger the electric field it creates.

## 4. What factors affect the electric field of a polarized atom?

The strength of the electric field of a polarized atom is affected by the magnitude of the dipole moment, the distance from the atom, and the dielectric constant of the surrounding medium.

## 5. Can the electric field of a polarized atom be shielded or cancelled out?

Yes, the electric field of a polarized atom can be shielded or cancelled out by introducing an opposite charge or by placing the atom in a medium with a high dielectric constant. This will disrupt the alignment of the atom's charges and weaken or eliminate the electric field.

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