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Chapter 4: Q4.30P (page 205)

An electric dipole p鈫�, pointing in the ydirection, is placed midwaybetween two large conducting plates, as shown in Fig. 4.33. Each plate makes a small angle 胃with respect to the xaxis, and they are maintained at potentials 卤V.What is the directionof the net force onp鈫�?(There's nothing to calculate,here, butdo explain your answer qualitatively.)

Short Answer

Expert verified

The net force onp鈫�placed midway between two large conducting plates is towards the right.

Step by step solution

01

Given data

There is a dipole with dipole moment p鈫�pointing in the ydirection and placed midway

between two large conducting plates.

The plate makes asmall angle 胃with respect to the xaxis.

The plates maintained at potentials 卤V.

02

Determine the direction of force on a dipole

The lines of force and the corresponding electric field are always perpendicular to a conducting surface.Thus, for the setup mentioned in the problem, the lines of follows emerge from the upper plate kept at a positive potential and go into the lower plate kept at a negative potential as follows

The corresponding direction of forces on the positive and negative ends of the dipole are also shown in the above figure.

Thus, the net force is towards the right.

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Most popular questions from this chapter

A point charge qis imbedded at the center of a sphere of linear dielectric material (with susceptibility蠂eand radius R).Find the electric field, the polarization, and the bound charge densities,蚁b and 蟽b.What is the total bound charge on the surface? Where is the compensating negative bound charge located?

An uncharged conducting sphere of radius ais coated with a thick

insulating shell (dielectric constant 蔚r) out to radius b.This object is now placed in an otherwise uniform electric field E鈫�0. Find the electric field in the insulator.

Calculate W,using both Eq. 4.55 and Eq. 4.58, for a sphere of radius

Rwith frozen-in uniform polarization P鈫� (Ex. 4.2). Comment on the discrepancy.

Which (if either) is the "true" energy of the system?

A conducting sphere at potential V0 is half embedded in linear dielectric material of susceptibility 蠂e, which occupies the regionz<0 (Fig. 4.35).

Claim:the potential everywhere is exactly the same as it would have been in the

absence of the dielectric! Check this claim, as follows:

  1. Write down the formula for the proposed potentialrole="math" localid="1657604498573" V(r),in terms ofV0,R,andr.Use it to determine the field, the polarization, the bound charge, and the free charge distribution on the sphere.
  2. Show that the resulting charge configuration would indeed produce the potentialV(r).
  3. Appeal to the uniqueness theorem in Prob. 4.38 to complete the argument.
  4. Could you solve the configurations in Fig. 4.36 with the same potential? If not, explain why.

A spherical conductor, of radius a,carries a charge Q(Fig. 4.29). It

is surrounded by linear dielectric material of susceptibilityXeout to radius b.Find the energy of this configuration (Eq. 4.58).
See all solutions

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