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Chapter 23: Q. 38- Excercises And Problems (page 655)

FIGUREP23.38shows three charges at the corners of a square. Write the electric field at point Pin component form.

Short Answer

Expert verified

The Electric filed at point isP=14πε0QL2(21)[i^+j^].

Step by step solution

01

Step: 1 Electric field:

The Electric fiels at point charge is

E=14πε0qr2r^

Electric field lines due to provided energies on a position Pand associated resolution along the x,yaxes are depicted in the diagram below.

02

Step: 2 Solving:

The electric field at point Ais,

E1=E1(i^)

The electric field magnitude of charge is

E1=14πε0QL2

Substituting and solving,

E1=14πε0QL2(i^)E1=14πε0QL2i^

03

Step: 3 Solvingfield at B:

The electric filed at corner Bis,

E2=E2xi^+E2yj^

The distance BPfrom the diagram is

BP=BC2+CP2

Substituting L=BC=CP

BP=L2+L2BP=2L

The magnitude at charge Bis

E2=14πε04QBP2

Substituting BP=2L

E2=14πε04Q(2L)2E2=14πε04Q2L2

04

Step; 4 Equating:

The horizontal component is

E2x=E2cos45

Substituting,

E2x=14πε04Q2L2cos45E2x=14πε04Q22L2

The vertical component is

E2y=E2sin45

Substituting,

E2y=14πε04Q2L2sin45E2y=14πε04Q22L2

05

Step: 5 Expression field:

The electric charge at corner is

E3=E3(j^)

The magnitude at charge is

E3=14πε0QL2

Substituting

E3=14πε0QL2(j^)

06

Step: 6 Net electric field:

The resultant horizontal direction is

Ex=E1+E2x

The net electric field is

E=Exi^+Eyj^

solving,

E=14πε0QL2+14πε04Q22L2i^+14πε0QL2+14πε04Q22L2j^E=14πε0QL2(1+2)i^+14πε0QL2(1+2)j^E=14πε0QL2(21)(i^+j^)

The net electric filed isP=14πε0QL2(21)[i^+j^].

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Most popular questions from this chapter

You’ve been assigned the task of determining the magnitude and direction of the electric field at a point in space. Give a step-by-step procedure of how you will do so. List any objects you will use, any measurements you will make, and any calculations you will need to perform. Make sure that your measurements do not disturb the charges that are creating the field.

An infinite plane of charge with surface charge density 3.2μC/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?

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

η2ε0[1-zz2+R2]=12η2ε0

In a classical model of the hydrogen atom, the electron orbits the proton in a circular orbit of radius0.053nm. What is the orbital frequency? The proton is so much more massive than the electron that you can assume the proton is at rest.

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?

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