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Chapter 3: Q3.7P (page 129)

Find the force on the charge +qin Fig. 3.14. (The xyplane is a grounded conductor.)

Short Answer

Expert verified

Answer

The net force on q is -14蟺蔚0(29272d2)z.

Step by step solution

01

Given data

Consider the given figure as shown below.

Here, from the given figure it is clear that xyplane is grounded conductor, thus potential is zero

02

Determine force

As +qinduces an equal and opposite charge of -qat a distance of Z=-3dand -2qinduces +2qat distance of Z=-d.

Write the expression for force on +qdue to -2q,.

F1=14蟺蔚0q(-2q)(2d)2z 鈥︹�� (1)

Write the expression for force on +qdue to +2q,.

F1=14蟺蔚0q(-2q)(4d)2z 鈥︹�� (2)

Write the expression for force on +qdue to -q.

F1=14蟺蔚0q(-2q)(6d)2z 鈥︹�� (3)

03

Determine the net force

Write the expression for the net force on q .

F=F1+F2+F3=q4蟺蔚0[-2q2d2+2q4d2+-q6d2]z=q24蟺蔚0[-12+18-136]z=q24蟺蔚0(29q272d2)z

Thus, the net force on q is -q24蟺蔚0(29q272d2)z.

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Most popular questions from this chapter

A solid sphere, radius R, is centered at the origin. The "northern" hemisphere carries a uniform charge density 蚁0, and the "southern" hemisphere a uniform charge density -蚁0鈥� Find the approximate field E(r,胃)for points far from the sphere (r>>R).

In Prob. 2.25, you found the potential on the axis of a uniformly charged disk:

V(r,0)=蟽2蔚0(r2+R2鈭�r)

(a) Use this, together with the fact that Pi(1)=1to evaluate the first three terms

in the expansion (Eq. 3.72) for the potential of the disk at points off the axis, assuming r>R.

(b) Find the potential for r<Rby the same method, using Eq. 3.66. [Note: You

must break the interior region up into two hemispheres, above and below the

disk. Do not assume the coefficients A1are the same in both hemispheres.]

A circular ring in thexy plane (radius R , centered at the origin) carries a uniform line charge 位. Find the first three terms(n=0,1,2) in the multi pole expansion for V(r,胃).

(a) Using the law of cosines, show that Eq. 3.17 can be written as follows:

V(r,胃)=14蟺蔚0[qr2+a2鈭�2racos鈦�胃鈭�qR2+(ra/R)2鈭�2racos鈦�胃]

Whererand 胃are the usual spherical polar coordinates, with the zaxis along the

line through q. In this form, it is obvious thatV=0on the sphere, localid="1657372270600" r=R.

(a) Find the induced surface charge on the sphere, as a function of 胃. Integrate this to get the total induced charge . (What should it be?)

(b) Calculate the energy of this configuration.

For the infinite slot (Ex. 3.3), determine the charge density 蟽(y)on

the strip at x=0, assuming it is a conductor at constant potential V0.
See all solutions

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