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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

You have a summer intern position with a company that designs and builds nanomachines. An engineer with the company is designing a microscopic oscillator to help keep time, and you’ve been assigned to help him analyze the design. He wants to place a negative charge at the center of a very small, positively charged metal ring. His claim is that the negative charge will undergo simple harmonic motion at a frequency determined by the amount of charge on the ring.

a. Consider a negative charge near the center of a positively charged ring centered on the z-axis. Show that there is a restoring force on the charge if it moves along the z-axisbut stays close to the center of the ring. That is, show there’s a force that tries to keep the charge at z=0. b. Show that for small oscillations, with amplitude <<R, a particle of mass mwith charge-qundergoes simple harmonic motion with frequency f=12πqQ4πε0mR3,RandQare the radius and charge of the ring.

c. Evaluate the oscillation frequency for an electron at the center of a 2.0μmdiameter ring charged to 1.0×10-13C.

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?

A 2.0-mm-diameter glass sphere has a charge of +1.0nC. What speed does an electron need to orbit the sphere 1.0mm above the surface?

An electric dipole is formed from two charges, ±q, spaced1.0cm apart. The dipole is at the origin, oriented along the y-axis. The electric field strength at the point x,y=(0cm,10cm)is 360N/C.

a. What is the charge q? Give your answer in nC.

b. What is the electric field strength at the pointx,y=10cm,0cm?

A10-cmlong thin glass rod uniformly charged to+10nCand a 10-cm-long thin plastic rod uniformly charged to-10nCare placed side by side, 4.0cmapart. What are the electric field strengthsE1toE3at distances1.0cm,2.0cm, and from the glass rod a3.0cmlong the line connecting the midpoints of the two rods?

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