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Chapter 15: Q10Q (page 616)

The rod in Figure 15.49 carries a uniformly distributed positive charge. Which arrow (a–h) best represents the direction of the electric field at the observation location marked with a red X?

Short Answer

Expert verified

Arrow hbest represents the direction of electric field at X.

Step by step solution

01

Given data

A rod with uniformly distributed positive charge.

02

Step 2:Electric field direction

Electric field from a positive charge distribution is directed away from the distribution.

03

Step 3:Determination ofthe direction of the field at the marked point

  • The rod can be divided into several small sections. Fields from sections to the left of point X will have two components, one pointed up and one pointed right. Similarly, fields from sections to the right of point X will have two components, one pointed up and one pointed left.
  • The net field will be the vector sum of all these fields. The upward components will all add up. The net horizontal component of the field can be obtained by subtracting the right components from the left.
  • Since the X mark is a bit shifted towards the left from the center, the sum of left components will be larger. The net field at X will thus have an upward component and a left component. This can be best represented by arrow h.

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Most popular questions from this chapter

A thin glass rod of length 80 cmis rubbed all over with wool and acquires a charge of 60 nC, distributed uniformly over its surface. Calculate the magnitude of the electric field due to the rod at a location 7 cmfrom the midpoint of the rod. Do the calculation two ways, first using the exact equation for a rod of any length, and second using the approximate equation for a long rod.

An electrostatic dust precipitator that is installed in a factory smokestack includes a straight metal wire of length L=0.8 mthat is charged approximately uniformly with a total charge Q=0.4×10-7C . A speck of coal dust (which is mostly carbon) is near the wire, far from both ends of the wire; the distance from the wire to the speck is d=1.5 cm . Carbon has an atomic mass of 12( 6protons and 6neutrons in the nucleus). A careful measurement of the polarizability of a carbon atom gives the value

∝=1.96×10-40C·mN/C

(a) Calculate the initial acceleration of the speck of coal dust, neglecting gravity. Explain your steps clearly. Your answer must be expressed in terms ofQ,L,d,and ∝. You can use other quantities in your calculations, but your final result must not include them. Don’t put numbers into your calculation until the very end, but then show the numerical calculation that you carry out on your calculator. It is convenient to use the “binomial expansion” that you may have learned in calculus, that(1+ε)n≈1+nεis ε≪1. Note thatcan be negative. (b) If the speck of coal dust were initially twice as far from the charged wire, how much smaller would be the initial acceleration of the speck?

If the total charge on a uniformly charged rod of length is 0.4 m is 2.2 nC, what is the magnitude of the electric field at a location 3 cm from the midpoint of the rod?

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.

A solid metal ball of radius 1.5 cm bearing a charge of −17 nC is located near a solid plastic ball of radius 2 cm bearing a uniformly distributed charge of +7 nC (Figure 15.62) on its outer surface. The distance between the centers of the balls is 9 cm. (a) Show the approximate charge distribution in and on each ball. (b) What is the electric field at the center of the metal ball due only to the charges on the plastic ball? (c) What is the net electric field at the center of the metal ball? (d) What is the electric field at the center of the metal ball due only to the charges on the surface of the metal ball?
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