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Chapter 23: Q.51 (page 656)

A parallel-plate capacitor has 2.0cm×2.0cmelectrodes with surface charge densities ±1.0×10−6C/m2. A proton traveling parallel to the electrodes at 1.0×106m/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.

Short Answer

Expert verified

The proton been deflected sideways when it reaches the far edge of the capacitor is

a=0.108×1014m2s

t=2×10−8sec

y=2.2mm

Step by step solution

01

Acceleration and Velocity

→η=1×10−6( charge densities)

From inside battery, there must be an electric current due to just a paired surface.

E=ηϵo=acceleration

a=qEmp

=qηϵomp

a=1.6×10−19×10−68.85×10−12×1.67×10−27

a=0.108×1014m2s

So there is no force as in downward motion, the pace is same:

d=vt

t=dv

=2×10−2106

=2×10−8sec

02

Distance

With in vertical motion, ion sweep area

y=ut+12at2

y=12×0.108×1014×2×10−82

y=2.2mm

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Most popular questions from this chapter

The ball in FIGURE Q23.10 is suspended from a large, uniformly charged positive plate. It swings with period T. If the ball is discharged, will the period increase, decrease, or stay the same? Explain.

Three charges are placed at the corners of the triangle in FIGURE Q23.15. The ++charge has twice the quantity of charge of the two - charges; the net charge is zero. Is the triangle in equilibrium? If so, explain why. If not, draw the equilibrium orientation.

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

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.

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

2.0×1012m/s2=(1.60×10-19C2)E(1.67×10-27kg)E=Q(8.85×10-12C2/Nm2)(0.020m)2Q
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