Chapter 2: Q 875865 2 4 (page 81)
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A certain ohmic resistor has a resistance of .A second resistor is made of the same material but is three times as long and has half the cross-sectional area. What is the resistance of the second resistor? What is the effective resistance of the two resistors in series?
Two very thin circular plastic sheets are close to each other and carry equal and opposite uniform charge. Explain briefly why the field between the sheets is much larger than the field outside. Illustrate your argument on a diagram.
Many heavy nuclei are “alpha emitters”: they emit an alpha particle, which is the historical name for the nucleus of a helium atom, which contains two protons. For example, a thorium nucleus containing 90 protons is an alpha-emitter. What element does thorium turn into as a result of emitting an alpha particle?
Apply the general results obtained in the full analysis of motion under the influence of a constant force in Section 2.5 to answer the following questions. You hold a small metal ball of mass m a height h above the floor. You let go, and the ball falls to the floor. Choose the origin of the coordinate system to be on the floor where the ball hits, with y up as usual. Just after release, what are yi and vyi? Just before hitting the floor, what is yf? How much time ∆t does it take for the ball to fall? What is vfy just before hitting the floor? Express all results in terms of m, g, and h. How would your results change if the ball had twice the mass?
Question: the Hall effect can be used to determine the sign of the mobile charges in a particular conducting material. A bar of a new kind of conducting material is connected to a battery as shown in Figure 20.85. In this diagram, the x-axis runs to the right, the y-axis runs up, and the z-axis runs out of the page, toward you. A voltmeter is connected across the bar as shown, with the leads placed directly opposite each other along a vertical line. In order to answer the following question, you should draw a careful diagram of the situation, including all relevant charges, electric fields, magnetic fields, and velocities.
Initially, there is no magnitude filed in the region of the bar. (a) Inside the bar, what is the direction of the electric field due to the charges on the batteries and the surface of the wires and the bar? This is the electric field that drives the current in the bar. (b) If the mobile charges in the bar are positive in what direction do they move when the current runs? (c) If the mobile charges in the bar are negative, in what direction do they move when the current runs? (d) In this situation (zero magnetic fields), what is the sign of the reading on the voltmeter?
Next, large coils (not shown) are moved near the bar. And current runs through the coils, making a magnetic field in the -z direction (into the page). (e) If the mobile charges in the bar are negative, what is the direction of the magnetic force on the mobile charge? (f) If the mobile charges in the bar are negative, which of the following things will happen? (1) Positive charge will accumulate on the top of the bar. (2) The bar will not becomes polarized. (3) Negative charge will accumulate on the left end of the bar. (4) Negative charge will accumulate on the top of the bar. (g) If the mobile charges in the bar are positive, what is the direction of the magnetic force on the mobile charges? (h) If the mobile charges in the bar are positive, which of these things will happen? (1) positive charge will accumulate on the top of the bar. (2) The bar will not becomes polarized. (3) Positive charge will accumulate on the right end of the bar. (4) Negative charge will accumulate on the top of the bar.
You look at the voltmeter and find that the reading on the meter is . (i) What can you conclude from this observation? (Remember that a voltmeter gives a positive reading if the positive lead is attached to the higher potential location.) (1) There is not enough information to figure out the sign of the mobile charges. (2) The mobile charges are negative. (3) The mobile charges are positive.
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