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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 -14πε0(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=14πε0q(-2q)(2d)2z …… (1)

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

F1=14πε0q(-2q)(4d)2z …… (2)

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

F1=14πε0q(-2q)(6d)2z …… (3)

03

Determine the net force

Write the expression for the net force on q .

F=F1+F2+F3=q4πε0[-2q2d2+2q4d2+-q6d2]z=q24πε0[-12+18-136]z=q24πε0(29q272d2)z

Thus, the net force on q is -q24πε0(29q272d2)z.

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Most popular questions from this chapter

Find the charge density σ(θ) on the surface of a sphere (radius R ) that

produces the same electric field, for points exterior to the sphere, as a charge qat the point a<R onthe zaxis.

A long cylindrical shell of radius Rcarries a uniform surface charge σ0on the upper half and an opposite charge -σ0on the lower half (Fig. 3.40). Find the electric potential inside and outside the cylinder.

You can use the superposition principle to combine solutions obtained by separation of variables. For example, in Prob. 3.16 you found the potential inside a cubical box, if five faces are grounded and the sixth is at a constant potential V0; by a six-fold superposition of the result, you could obtain the potential inside a cube with the faces maintained at specified constant voltages . V1,V2,......V6In this way, using Ex. 3.4 and Prob. 3.15, find the potential inside a rectangular pipe with two facing sides (x=±b)at potential V0, a third (y=a)at V1. and the last at(y=a) grounded.

A conducting sphere of radius a, at potential, is surrounded by a

thin concentric spherical shell of radius b,over which someone has glued a surface charge

σθ=kcosθ

whereis a constant and is the usual spherical coordinate.

a. Find the potential in each region: (i) r>b, and (ii) a<r<b.

b. Find the induced surface chargeσiθon the conductor.

c. What is the total charge of this system? Check that your answer is consistent with the behavior of V at large.

A spherical shell of radius carries a uniform surface charge on the "northern" hemisphere and a uniform surface charge on the "southern "hemisphere. Find the potential inside and outside the sphere, calculating the coefficients explicitly up to and .
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