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Chapter 23: Q. 18 (page 654)

A20cm脳20cmhorizontal metal electrode is uniformly charged to +80nC. What is the electric field strength 2.0mmabove the center of the electrode?

Short Answer

Expert verified

The electric field strength has the magnitude of1.1路105N/Cand it is perpendicular to the electrode pointing away from it.

Step by step solution

01

Plane for electric field strength

02

Area of electrode and surface charge density

The given distance 2mmhas no bearing on the rest of the problem.

It is solely used to justify the use of plane formulas despite the electrode's finite size.

Let a=20cm.

Then the area of the electrode is,

A=a2

The surface charge density is,

蟽=qA=qa2

03

Calculation for electric field

Whereq=80nC,

The equally charged plane generates a consistent electric field in all directions, regardless of distance from the plane.

This field is perpendicular to the plane, points away from it when the plane is charged positively, and has a magnitude of,

E=蟽2蔚0

In this scenario, we have an electric field.

E=q2a2蔚0

Substituting given values,

we can find,

E=80nc2(20cm)(20cm)(8.8541878128(13)脳10-12)

E=1.1路105N/C

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Most popular questions from this chapter

Air "breaks down" when the electric field strength reaches 3.0脳106N/c, causing a spark. A parallel-plate capacitor is made from two 4.0cm脳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 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?

Charge Q is uniformly distributed along a thin, flexible rod of length L. The rod is then bent into the semicircle shown in FIGURE. 23.47

a. Find an expression for the electric field E鈫�at the center of the semicircle.

Hint: A small piece of arc length 螖sspans a small angle 螖胃=螖s/R, where Ris the radius.

b. Evaluate the field strength if localid="1651169583117" L=10cmand localid="1651169587457" Q=30nC.

An electron traveling parallel to a uniform electric field increases its speed from 2.0脳107m/sto4.0脳107m/s over a distance of 1.2cm. What is the electric field strength?

A small segment of wire in FIGURE Q23.4contains 10nCof charge.

a. The segment is shrunk to one-third of its original length. What is the ratio of 位f/位i, where 位iand位f are the initial and final linear charge densities?

b. A proton is very far from the wire. What is the ratio Ff /Fi of the electric force on the proton after the segment is shrunk to the force before the segment was shrunk?

c. Suppose the original segment of wire is stretched to 10 times its original length. How much charge must be added to the wire to keep the linear charge density unchanged?
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