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Chapter 15: Q55P (page 622)

Question: A glass sphere carrying a uniformly distributed charge of 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鈥檛 there? Explain briefly. (d) Now suppose that the glass sphere carrying a uniform charge of 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 outside the metal shell larger, smaller, or the same as it would be if the metal shell weren鈥檛 there? Explain briefly.

Short Answer

Expert verified

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鈥檛 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鈥檛 there.

Step by step solution

01

Identification of given data

The given data can be listed below as:

The charge carried by the glass sphere is +Q

02

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.

03

(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.

04

(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鈥檚 surface. The core has then zero amount of charge.

Thus, the inner glass sphere will not be polarized.

05

(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鈥檛 there.

06

(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.

07

(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 will be on the outer surface and will be on the inner surface of the sphere.

Thus, the assertion is proved.

08

(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鈥檛 there.

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Most popular questions from this chapter

An electrostatic dust precipitator that is installed in a factory smokestack includes a straight metal wire of length L=0.8 mthat is charged approximately uniformly with a total charge Q=0.4脳10-7C . A speck of coal dust (which is mostly carbon) is near the wire, far from both ends of the wire; the distance from the wire to the speck is d=1.5 cm . Carbon has an atomic mass of 12( 6protons and 6neutrons in the nucleus). A careful measurement of the polarizability of a carbon atom gives the value

鈭�=1.96脳10-40C路mN/C

(a) Calculate the initial acceleration of the speck of coal dust, neglecting gravity. Explain your steps clearly. Your answer must be expressed in terms ofQ,L,d,and 鈭�. You can use other quantities in your calculations, but your final result must not include them. Don鈥檛 put numbers into your calculation until the very end, but then show the numerical calculation that you carry out on your calculator. It is convenient to use the 鈥渂inomial expansion鈥� that you may have learned in calculus, that(1+蔚)n鈮�1+苍蔚is 蔚鈮�1. Note thatcan be negative. (b) If the speck of coal dust were initially twice as far from the charged wire, how much smaller would be the initial acceleration of the speck?

If the magnitude of the electric field in air exceeds roughly3脳10-6N/C, the air breaks down and a spark forms. For a two-disk capacitor of radius50cmwith a gap of role="math" localid="1656068507772" 1mm, what is the maximum charge (plus and minus) that can be placed on the disks without a spark forming (which would permit charge to flow from one disk to the other)? Under these conditions, what is the strength of the fringe field just outside the center of the capacitor?

A rod is 2.5m long. Its charge is -2脳10-7C. The observation location is 4cm from the rod, in the mid plane. In the expression

E=14蟺蔚0Qrr2+(L2)2

what isr in meters?

In Figure 15.61 are two uniformly charged disks of radius R that are very close to each other (gap鈮猂). The disk on the left has a charge of鈭�Qleftand the disk on the right has a charge of +Qright(Qrightis greater thanQleft). A uniformly charged thin rod of length L lies at the edge of the disks, parallel to the axis of the disks and cantered on the gap. The rod has a charge of +Qrod.

(a) Calculate the magnitude and direction of the electric field at the point marked 脳 at the center of the gap region, and explain briefly, including showing the electric field on a diagram. Your results must not contain any symbols other than the given quantities R,Qleft, Qright, L, andQrod(and fundamental constants), unless you define intermediate results in terms of the given quantities. (b) If an electron is placed at the center of the gap region, what are the magnitude and direction of the electric force that acts on the electron?

If the total charge on a thin rod of length0.4mis 2.5n/C, what is the magnitude of the electric field at a location1Cmfrom the midpoint of the rod, perpendicular to the rod?
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