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An electron is launched at a 45angle and a speed of 5.0×106m/sfrom the positive plate of the parallel-plate capacitor shown in FIGURE P23.52. The electron lands 4.0cmaway.

a. What is the electric field strength inside the capacitor?

b. What is the smallest possible spacing between the plates?

Short Answer

Expert verified

a. The electric field strength inside the capacitor isa=6.3×1014m/s2

b. The smallest possible spacing between the plates is

E=3.6×103N/C

H=1cm

Step by step solution

01

Velocity (part a)

The pace as in downward motion Vocos45.

And there is no stress with in downward motion

so,

d=Vocos45×t.

t=dVocos45

localid="1650219090644" =4×102m×25×106m/s×1

=1.13×108s

At its highest point (vertical direction).

vf=0

v=uatt=t2=0.56×108s(a opposite to Force

a=ua

=Vosinθt

localid="1650219122312" =5×106m/s2×0.56×108s

a=6.3×1014m/s2

02

Force (part b)

Force is,

eE=ma

ma=eE~E

=mae

localid="1650219349035" role="math" =9.11×1031kg×6.3×1014m/s21.6×1019C

E=3.6×103N/C

MaximumH

v2=uv22aH

H=uv22a

localid="1650219390403" =52×10622×6.3×1014m/s2

=1×102m

H=1cm

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Most popular questions from this chapter

Two 2.0-cmdiameter disks face each other, 1.0mmapart. They are charged to ±10nC.

a. What is the electric field strength between the disks?

b. A proton is shot from the negative disk toward the positive disk. What launch speed must the proton have to just barely reach the positive disk?

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.

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a. Find an expression for the electric field Eat the center of the semicircle.

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You've hung two very large sheets of plastic facing each other with distancedbetween them, as shown inFIGUREEX23.20. By rubbing them with wool and silk, you've managed to give one sheet a uniform surface charge density and the other a uniη1=-η0form surface charge density η2=+3η0. What are the electric field vectors at points1,2and3?

A small object is released at point 3in the center of the capacitor in FIGURE Q23.11. For each situation, does the object move to the right, to the left, or remain in place? If it moves, does it accelerate or move at constant speed?

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