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Chapter 14: Q25Q (page 580)

Metal sphere A is charged negatively and then brought near an uncharged metal sphere B (Figure 14.78). Both spheres rest on insulating supports, and the humidity is very low.

(a) Use +鈥檚 and 鈭掆�檚 to show the approximate distribution of charges on the two spheres. (Hint: Think hard about both spheres, not just B.)

(b) A small, lightweight hollow metal ball, initially uncharged, is suspended from a string and hung between the two spheres (Figure 14.79). It is observed that the ball swings rapidly back and forth hitting one sphere and then the other. This goes on for seconds, but then the ball stops swinging and hangs between the two spheres. Explain in detail, step by step, why the ball swings back and forth and why it finally stops swinging. Your explanation must include good physics diagrams.

Short Answer

Expert verified

a) Sphere B will get about of a negative charge, and sphere A will have about of negative charge.

b) Due to the charge distribution from sphere A to sphere B, the ball is moving towards sphere B, and as sphere B is producing an equal and opposite force on sphere A, the ball is moving to sphere A with this. Finally, when both the spheres are of equal charge, the ball stops moving as there is no charge distribution.

Step by step solution

01

Identification of the given data

The given data can be listed below as follows,

  • The metal sphere A is negatively charged.
  • The metal sphere B is uncharged.
  • The ball has swung for 5s.
02

Significance of the induction charging

Charging by induction illustrates that an uncharged particle gets charged if it is kept beside the charged particle.

Also, induction charging is described as a process in which an object can be changed without touching it.

The induction charging gives the charge distribution of the spheres and why the ball moved back and forth.

03

Determination of the charge distribution of the spheres

(a)

According to the law of induction, the charged sphere distributes charge to the uncharged sphere until both the spheres get an equal charge. Hence, both the spheres get an equal amount of negative charge due to the charging by induction.

As sphere A is negatively charged and sphere B is uncharged, the charge will flow from sphere A to sphere B according to the induction charging. The charge flowing will continue until both the spheres鈥� charge remains equal.

Thus, sphere B will get about amount of negative charge, and sphere A will have about amount of negative charge.

04

Determination of the motion of the ball

(b)

The diagram of the spheres has been drawn below,

The above diagrams have shown how the lightweight hollow metal ball is swinging back and forth and stops eventually. Here, in figure 1, when the charge of the sphere A is going towards the sphere B, the ball is also moving and goes towards the sphere B as it was also uncharged. Moreover, according to Newton鈥檚 third law, sphere B exerts an equal and opposite force on sphere A which causes the ball to move to sphere A which is shown in figure 2. Hence, in figure 1 and figure 2, the ball moves due to the charge distribution between the spheres.

Finally, in figure 3, when both the spheres become equally charged, there is no charge distribution, and the ball hangs still. Hence, the ball is swinging back and forth because of the unequal distribution of charges, and when the distribution of the charges becomes equal, the ball stops swinging. Hence, in figure 3, as the charge distribution between the spheres stopped, the ball stopped moving.

Thus, due to the charge distribution from sphere A to sphere B, the ball is moving towards sphere B, and as sphere B is producing an equal and opposite force on sphere A, the ball is moving to sphere A with this. Finally, when both spheres have equal charge, the ball stops moving as there is no unequal charge.

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Most popular questions from this chapter

: A thin, hollow spherical plastic shell of radius \({\bf{R}}\)carries a uniformly distributed negative charge \({\bf{ - Q}}\). A slice through the plastic shell is shown in Figure 14.95. To the left of the spherical shell are four charges packed closely together as shown (the distance \({\bf{s}}\) is shown greatly enlarged for clarity). The distance from the center of the four charges to the center of the plastic shell is \({\bf{L}}\) , which is much larger than \({\bf{s}}\left( {{\bf{L}} \gg {\bf{s}}} \right)\). Remember that a uniformly charged sphere makes an electric field as though all the charge were concentrated at the center of the sphere.

(a)Calculate the \({\bf{x}}\) and \({\bf{y}}\) components of the electric field at location B, a distance \({\bf{b}}\) to the right of the outer surface of the plastic shell. Explain briefly, including showing the electric field on a diagram. Your results should not contain any symbols other than the given quantities \({\bf{R,Q,q,s,L}}\), and \({\bf{b}}\)(and fundamental constants). You need not simplify the final algebraic results except for taking into account the fact that \({\bf{L}} \gg {\bf{s}}\).

(b)What simplifying assumption did you have to make in part (a)?

(c)The plastic shell is removed and replaced by an uncharged metal ball, as in Figure 14.96. At location Ainside the metal ball, a distance \({\bf{b}}\)to the left of the outer surface of the ball, accurately draw and label the electric field\({{\bf{\vec E}}_{{\bf{ball}}}}\) due to the ball charges and the electric field \({{\bf{\vec E}}_{\bf{4}}}\) of the four charges. Explain briefly.

(d)Show the distribution of ball charges.

(e)Calculate the \({\bf{x}}\) and \({\bf{y}}\) components of the net electric field at location A.

The mobility of Na+ions in water is5.2脳10-8(m/s)(N/C). If an electric field of2400N/Cis maintained in the fluid, what is the drift speed of the sodium ions?

A solid plastic ball has negative charge uniformly spread over its surface. Which of the diagrams in Figure 14.85 best shows the polarization of molecules inside the ball?

An electric field of magnitude 190鈥�鈥�N/C is applied to a solution containing chloride ions. The mobility of chloride ions in solution is 7.91脳10-8鈥�鈥�(m/s)/(N/C).What is the average drift speed of the chloride ions in the solution?

A glass sphere carrying a uniformly distributed charge of +Qis 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 +Qis 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 P outside the metal shell larger, smaller, or the same as it would be if the metal shell weren鈥檛 there? Explain briefly.
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