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Chapter 15: Q7Q (page 616)

When calculating the electric field of an object with electric charge distributed approximately uniformly over its surface, what is the order in which you should do the following operations? (1) Check the direction and units. (2) Write an expression for the electric field due to one point-like piece of the object. (3) Divide up the object into small pieces of a shape whose field is known. (4) Sum the vector contributions of all the pieces.

Short Answer

Expert verified

Answer

The order of doing the following operation is (3)-(2)-(4)-(1).

Step by step solution

01

Significance of an electric charge

The electric charge is described as the physical property of a matter that helps to induce a force when placed inside a particular electromagnetic field. There are two types of the electric charges mainly positive and negative charges.

02

Determination of the right order of doing the operations

The first and the foremost step for calculating the electric field of an object is to divide the objects into small pieces whose electric field is known. The second step write the expression of the electric field of that object. The third step is adding the vector contributions of the pieces. The final step is to checking the units and directions in order to check the results.

Thus, the order of doing the following operation is (3)-(2)-(4)-(1).

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Most popular questions from this chapter

A capacitor made of two parallel uniformly charged circular metal disks carries a charge of +Q and 鈭扱 on the inner surfaces of the plates and very small amounts of charge +q and 鈭抭 on the outer surfaces of the plates. Each plate has a radius R and thickness t, and the gap distance between the plates is s. How much charge q is on the outside surface of the positive disk, in terms of Q?

In Figure 15.61 are two uniformly charged disks of radius R that are very close to each other (gap鈮猂). The disk on the left has a charge of鈭�Qleftand the disk on the right has a charge of +Qright(Qrightis greater thanQleft). A uniformly charged thin rod of length L lies at the edge of the disks, parallel to the axis of the disks and cantered on the gap. The rod has a charge of +Qrod.

(a) Calculate the magnitude and direction of the electric field at the point marked 脳 at the center of the gap region, and explain briefly, including showing the electric field on a diagram. Your results must not contain any symbols other than the given quantities R,Qleft, Qright, L, andQrod(and fundamental constants), unless you define intermediate results in terms of the given quantities. (b) If an electron is placed at the center of the gap region, what are the magnitude and direction of the electric force that acts on the electron?

A solid plastic sphere of radius R1has a charge -Q1on its surface (Figure 15.70). A concentric spherical metal shell of inner radius R2and outer radius R3carries a charge Q2on the inner surface and a charge Q3on the outer surface. Q1, Q2, and Q3are positive numbers, and the total charge Q2+Q3on the metal shell is greater than Q1.

At an observation location a distance rfrom the center, determine the magnitude and direction of the electric field in the following regions, and explain briefly in each case. For parts role="math" localid="1656931802199" a-d, be sure to give both the direction and the magnitude of the electric field, and explain briefly: (a)role="math" localid="1656932347681" r<R1(inside the plastic sphere), (b)role="math" localid="1656932286893" R1<r<R2(in the air gap), (c)role="math" localid="1656932322994" R<r<R(in the metal),(d)role="math" localid="1656932390135" r>R3(outside the metal).(e) Supposerole="math" localid="1656932377163" -Q1=-5nC. What isrole="math" localid="1656932400004" Q2? Explain fully on the basis of fundamental principles. (f) What can you say about the molecular polarization in the plastic? Explain briefly. Include a drawing if appropriate.

In a cathode-ray tube, an electron travels in a vacuum and enters a region between two deflection plates where there is an upward electric field of magnitude1脳105N/C(Figure 15.60).


(a) Sketch the trajectory of the electron, continuing on well past the deflection plates (the electron is going fast enough that it does not strike the plates). (b) Calculate the acceleration of the electron while it is between the deflection plates. (c) The deflection plates measure 12 cm by 3 cm, and the gap between them is 2.5 mm. The plates are charged equally and oppositely. What are the magnitude and sign of the charge on the upper plate?

You stand at location A, a distance d from the origin, and hold a small charged ball. You find that the electric force on the ball is 0.08 N. You move to location B, a distance 2d from the origin, and find the electric force on the ball to be 0.04 N. What object located at the origin might be the source of the field? (1) A point charge, (2) A dipole, (3) A uniformly charged rod, (4) A uniformly charged ring, (5) A uniformly charged disk, (6) A capacitor, (7) A uniformly charged hollow sphere, (8) None of the above If the force at B were 0.0799 N, what would be your answer? If the force at B were 0.01 N, what would be your answer? If the force at B were 0.02 N, what would be your answer?
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