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Chapter 23: Q. 13 (page 653)
A long thin rod has the nonuniform charge density , where localid="1648623923714" is measured from the center of the rod. What is the total charge on the rod?
Hint: This exercise requires an integration. Think about how to handle the absolute value sign.
The total charge on the rod is is.
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The ball in FIGURE is suspended from a large, uniformly charged positive plate. It swings with period T. If the ball is discharged, will the period increase, decrease, or stay the same? Explain.
An electric field can induce an electric dipole in a neutral atom or molecule by pushing the positive and negative charges in opposite directions. The dipole moment of an induced dipole is directly proportional to the electric field. That is, , where is called the polarizability of the molecule. A bigger field stretches the molecule farther and causes a larger dipole moment.
a. What are the units of ?
b. An ion with charge is distancefrom a molecule with polarizability . Find an expression for the force .
Twodiameter charged rings face each other,apart. Both rings are charged to. What is the electric field strength at (a) the midpoint between the two rings and (b) the center of the left ring?
A problem of practical interest is to make a beam of electrons turn a corner. This can be done with the parallel-plate capacitor shown in FIGURE. An electron with kinetic energy enters through a small hole in the bottom plate of the capacitor.
a. Should the bottom plate be charged positive or negative relative to the top plate if you want the electron to turn to the right? Explain.
b. What strength electric field is needed if the electron is to emerge from an exit hole away from the entrance hole, traveling at right angles to its original direction?
Hint: The difficulty of this problem depends on how you choose your coordinate system.
c. What minimum separation must the capacitor plates have?
A -diameter oil droplet (density role="math" localid="1649088632675" ) is negatively charged with the addition of extra electrons. It is released from rest from a very wide plane of positive charge, after which it accelerates toward the plane and collides with a speed of . What is the surface charge density of the plane?
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