Question

A glass sphere carrying a uniformly distributed charge of $\mathbf{+}\mathit{Q}$is surrounded by an initially neutral spherical plastic shell (Figure 15.67).

(a) Qualitatively, indicate the polarization of the plastic. (b) Qualitatively, indicate the polarization of the inner glass sphere. Explain briefly. (c) Is the electric field at location P outside the plastic shell larger, smaller, or the same as it would be if the plastic weren’t there? Explain briefly. (d) Now suppose that the glass sphere carrying a uniform charge of $\mathbf{+}\mathit{Q}$is surrounded by an initially neutral metal shell (Figure 15.68). Qualitatively, indicate the polarization of the metal.

e) Now be quantitative about the polarization of the metal sphere and prove your assertions. (f) Is the electric field at location $\mathit{P}$ outside the metal shell larger, smaller, or the same as it would be if the metal shell weren’t there? Explain briefly.

Short answer

Answer

(a) The dipoles inside the plastic will be polarized and their negative ends will point towards the center radially.

(b) The inner glass sphere will not be polarized.

(c) The electric field at location P outside the plastic shell is same as it would be if the plastic weren’t there.

(d) The negative charges will move towards the inner surface and the positive charge will move toward the outer surface.

(e) The assertion is proved.

(f) The electric field at location P outside the plastic shell is same as it would be if the metal shell weren’t there.

Step-by-step solution

Identification of given data

The given data can be listed below as:

The charge carried by the glass sphere is $\mathbf{+}\mathit{Q}$.

Significance of the polarization

The polarization is described as the property of the electromagnetic type of radiation, that helps to relate the magnitude and the direction of the electric field. However, polarization occurs when the negative electron cloud surrounds positive nuclei of atom.

(a) Determination of the polarization of the plastic initially

Here, it has been observed that the dipoles inside the plastic will be polarized and also orient towards themselves radially. However, the dipoles will orient pointing the negative charges towards the center.

Thus, the dipoles inside the plastic will be polarized and their negative ends will point towards the center radially.

(b) Determination of the polarization of the inner glass sphere

The net electric field inside the glass sphere is zero. Hence, there will not be any polarization. The charges are distributed inside the charged hollow conductor’s surface. The core has then zero amount of charge.

Thus, the inner glass sphere will not be polarized.

(c) Determination of the size of the electric field at the location P due to the plastic sphere

The positive charges mainly get displaced during the polarization which are closer to the location P than the negatively charged particle. Hence, as the positive charges are displaced and if the plastic is not there, then the size of the electric field will be the same.

Thus, the electric field at location P outside the plastic shell is same as it would be if the plastic weren’t there.

(d) Determination of the polarization of the metal finally

Here, from the given figure, it has been observed that the charge of the glass sphere is being surrounded by a neutral shell of metal. The polarization of the positive charges is mainly directed outwards and the polarization of the negative charges are mainly directed inward.

Thus, the negative charges will move towards the inner surface and the positive charge will move toward the outer surface.

(e) Prove of the assertions made in the point (d)

As the glass sphere has been surrounded by a neutral metal shell, then the metal shell will be charged. However, it has been observed that the electric field of the positive charge is directed outward and the negative charge is directed inward. Hence, the charge $\mathbf{+}\mathit{Q}$will be on the outer surface and $\mathbf{-}\mathit{Q}$will be on the inner surface of the sphere.

Thus, the assertion is proved.

(f) Determination of the size of the electric field at the location P due to the metal sphere

The positive charges mainly get displaced during the polarization which are closer to location P than the negatively charged particle. Hence, as the positive charges are displaced and if the metal shell is not there, then the size of the electric field will be the same.

Thus, the electric field at location P outside the plastic shell is same as it would be if the metal shell weren’t there.