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Chapter 23: Q. 5 (page 652)

An electron experiences a force of magnitude F when it is1cmfrom a very long, charged wire with linear charge density位. If the charge density is doubled, at what distance from the wire will a proton experience a force of the same magnitudeF?

Short Answer

Expert verified

The amount of distance from the wire when a proton experiences a force of the same magnitude F from the wire=2脳10-2m.

Step by step solution

01

Given information

For an electron: r1=1cm=10-2m

Charge of electron=-q

Linear charge density in case of electron位1=位

Charge of proton=+q

Linear charge density位2=2位

02

Explanation

F=-e2位4蟺e010-2鈬�F=e2(2位)4蟺e0r2鈬�-e2位4蟺e010-2=e2(2位)4蟺e0r2r2=-2脳10-2mr2=2脳10-2m

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Most popular questions from this chapter

The combustion of fossil fuels produces micron-sized particles of soot, one of the major components of air pollution. The terminal speeds of these particles are extremely small, so they remain suspended in air for very long periods of time. Furthermore, very small particles almost always acquire small amounts of charge from cosmic rays and various atmospheric effects, so their motion is influenced not only by gravity but also by the earth's weak electric field. Consider a small spherical particle of radius r, density 蚁, and charge q. A small sphere moving with speed v experiences a drag force Fdrag=6蟺畏rv, where 畏 is the viscosity of the air. (This differs from the drag force you learned in Chapter 6 because there we considered macroscopic rather than microscopic objects.)

a. A particle falling at its terminal speed vtermis in equilibrium with no net force. Write Newton's first law for this particle falling in the presence of a downward electric field of strength E, then solve to find an expression for vterm.

b. Soot is primarily carbon, and carbon in the form of graphite has a density of 2200kg/m3. In the absence of an electric field, what is the terminal speed in mm/s of a 1.0-渭m-diameter graphite particle? The viscosity of air at 20掳C is 1.8脳10-5kg/ms.

c. The earth's electric field is typically (150 N/C , downward). In this field, what is the terminal speed in mm/s of a 1.0 渭m-diameter graphite particle that has acquired 250 extra electrons?

A parallel-plate capacitor has 2.0cm脳2.0cmelectrodes with surface charge densities 卤1.0脳10鈭�6C/m2. A proton traveling parallel to the electrodes at 1.0脳106m/s enters the center of the gap between them. By what distance has the proton been deflected sideways when it reaches the far edge of the capacitor? Assume the field is uniform inside the capacitor and zero outside the capacitor.

A parallel-plate capacitor consists of two square plates, size L脳L, separated by distance d. The plates are given charge卤Q. What is the ratio Ef/Eiof the final to initial electric field strengths if

(a) Q is doubled,

(b)L is doubled, and

(c) d is doubled? Each part changes only one quantity; the other quantities have their initial values

A small object is released at point 3in the center of the capacitor in FIGURE Q23.11. For each situation, does the object move to the right, to the left, or remain in place? If it moves, does it accelerate or move at constant speed?

a. A positive object is released from rest.

b. A neutral but polarizable object is released from rest.

c. A negative object is released from rest.

An infinite plane of charge with surface charge density 3.2渭C/m2has a 20-cm-diameter circular hole cut out of it. What is the electric field strength directly over the center of the hole at a distance of 12cm?

Hint: Can you create this charge distribution as a superposition of charge distributions for which you know the electric field?
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