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In Problems 63 through 66 you are given the equation(s) used to solve a problem. For each of these

a. Write a realistic problem for which this is the correct equation(s).

b. Finish the solution of the problem

(9.0×109Nm2/C2)2(2.0×10-7C/m)r=25000N/C

Short Answer

Expert verified

(a) Find the Electric field strength at point Pon the rod's axis at distance rfrom the center of an infinite charge rod, with the linear charge density is2×10-7C/min 25000N/C

(b) The solution is0.144m

Step by step solution

01

Given information and formula used

Given :

(9.0×109Nm2/C2)2(2.0×10-7C/m)r=25000N/C

Theory used :

TheElectric field of an infinite line charge with a uniform linear charge density can be obtained by a using Gauss' law. Considering a Gaussian surface in the form of a cylinder at radius r, the electric field has the same magnitude at every point of the cylinder and is directed outward.

02

Writing a realistic problem and finding the solution of the problem 

(a) Realistic problem :

On an infinite charge rod, let the linear charge density is 2×10-7C/m.

In 25000N/C, find the electric field strength at point Pon the rod's axis at distance rfrom the center.

(b) Solution :

(9.0×109Nm2/C2)2(2.0×10-7C/m)r=25000N/Cr=(9.0×109Nm2/C2)2(2.0×10-7C/m)25000N/C=0.144m

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Most popular questions from this chapter

A sphere of radius Rand surface charge density ηis positioned with its center distance 2R from an infinite plane with surface charge density η. At what distance from the plane, along a line toward the center of the sphere, is the electric field zero?

FIGURE shows a thin rod of length Lwith total charge Q.

a. Find an expression for the electric field strength at point Pon the axis of the rod at distance rfrom the center.

b. Verify that your expression has the expected behavior if rL.

c. Evaluate Eat r=3.0cmif L=5.0cmand Q=3.0nC.

Air "breaks down" when the electric field strength reaches 3.0×106N/c, causing a spark. A parallel-plate capacitor is made from two 4.0cm×4.0cm electrodes. How many electrons must be transferred from one electrode to the other to create a spark between the electrodes?

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 ρ, and charge q. A small sphere moving with speed v experiences a drag force Fdrag=6πηrv, where η 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-μm-diameter graphite particle? The viscosity of air at 20°C is 1.8×10-5kg/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 μm-diameter graphite particle that has acquired 250 extra electrons?

One type of ink-jet printer, called an electrostatic ink-jet printer, forms the letters by using deflecting electrodes to steer charged ink drops up and down vertically as the ink jet sweeps horizontally across the page. The ink jet forms30μm diameter drops of ink, charges them by spraying 800,000 electrons on the surface, and shoots them toward the page at a speed of 20m/s. Along the way, the drops pass through two horizontal, parallel electrodes that are 6.0mmlong,4.0mm wide, and spaced 1.0mm apart. The distance from the center of the electrodes to the paper is 2.0cm. To form the tallest letters, which have a height of 6.0mm, the drops need to be deflected upward (or downward) by 3.0mm. What electric field strength is needed between the electrodes to achieve this deflection? Ink, which consists of dye particles suspended in alcohol, has a density of 800kg/m3 .

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