Logout Open In App
Open In App
Warning: foreach() argument must be of type array|object, bool given in /var/www/html/web/app/themes/studypress-core-theme/template-parts/header/mobile-offcanvas.php on line 20

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 +’s and −’s 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’ 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’s 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.

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

(a)The positively charged particle shown in diagram 1 in Figure 14.94 creates an electric field \({{\bf{\vec E}}_{\bf{p}}}\) at location A. Which of the arrows (a–j) in Figure 14.94 best indicates the direction of \({{\bf{\vec E}}_{\bf{p}}}\) at location A?

(b)Now a block of metal is placed in the location shown in diagram 2 in Figure 14.94. Which of the arrows (a–j) in Figure 14.94 best indicates the direction of the electric field \({{\bf{\vec E}}_{\bf{m}}}\) at location Adue only to the charges in and/or on the metal block?

(c)\(\left| {{{{\bf{\vec E}}}_{\bf{p}}}} \right|\)is greater than \(\left| {{{{\bf{\vec E}}}_{\bf{m}}}} \right|\). With the metal block still in place, which of the arrows (a–j) in Figure 14.94 best indicates the direction of the net electric field at location A?

(d)With the metal block still in place, which of the following statements about the magnitude of \({{\bf{\vec E}}_{\bf{p}}}\), the field due only to the charged particle, is correct?

(1) \(\left| {{{{\bf{\vec E}}}_{\bf{p}}}} \right|\)is less than it was originally, because the block is in the way.

(2) \(\left| {{{{\bf{\vec E}}}_{\bf{p}}}} \right|\)is the same as it was originally, without the block.

(3) \(\left| {{{{\bf{\vec E}}}_{\bf{p}}}} \right|\)is zero, because the electric field due to the particle can’t go through the block.

(e)With the metal block still in place, how does the magnitude of\({{\bf{\vec E}}_{{\bf{net}}}}\) at location Acompare to the magnitude of \({{\bf{\vec E}}_{\bf{p}}}\)?

(f)Which of the arrows (a–j) in Figure 14.94 best indicates the direction of the net electric field at the center of the metal block (inside the metal)?

You rub a clear plastic pen with wool, and observe that a strip of invisible tape is attracted to the pen. Assuming that the pen has a net negative charge, which of the following could be true? Select all that apply. (1) The tape might be negatively charged. (2) The tape might be positively charged. (3) The tape might be uncharged. (4) There is not enough information to conclude anything.

Is the following statement true or false? If true, what principle makes it true? If false, give a counterexample or say why. See Figure 14.67.

“The electric field Epointat the center of an induced dipole, due to the point charge, is equal in magnitude and opposite in direction to the electric field Edipoleat the location of the point charge, due to the induced dipole.”

You rub a plastic comb through your hair and it now carries a charge of -4×10-10C. What is the charge on your hair?

A very thin spherical plastic shell of radius15 cm carries a uniformly distributed negative charge of −8 nC(−8×10−9 C)on its outer surface (so it makes an electric field as though all the charge were concentrated at the center of the sphere). An uncharged solid metal block is placed nearby. The block is10cm thick, and it is10cm away from the surface of the sphere. See Figure 14.97. (a) Sketch the approximate charge distribution of the neutral solid metal block.

(b) Draw the electric field vector at the center of the metal block that is due solely to the charge distribution you sketched (that is, excluding the contributions of the sphere).

(c) Calculate the magnitude of the electric field vector you drew. Explain briefly. If you must make any approximations, state what they are.
See all solutions

Recommended explanations on Physics Textbooks

Electric Charge Field and Potential

Read Explanation

Physical Quantities And Units

Read Explanation

Scientific Method Physics

Read Explanation

Oscillations

Read Explanation

Measurements

Read Explanation

Astrophysics

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.

Sign-up for free