Introduction To Health Physics
Introduction To Health Physics
5th Edition
ISBN: 9780071835275
Author: Johnson, Thomas E. (thomas Edward), Cember, Herman.
Publisher: Mcgraw-hill Education,
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Chapter 2, Problem 2.18P

(a)

To determine

With what velocity does the electron strike the positive plate if a cylindrical capacitor is made of two coaxial conductors—the outer one’s diameter is 20.2 mm and the inner one’s diameter is 0.2 mm; the inner conductor is 1000-V positive with respect to the outer conductor?

(a)

Expert Solution
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Explanation of Solution

Given info:.

V=1000Vd=0.01mm=9.11×1031kgq=1.602×1019C.

Formula used:.

Kinetic energy

KE=12mv2.

Potential energy

PE=qV.

Calculation:.

We have,

12mv2=qVv=2qVm=2×1.602×1019×10009.11×1031=1.9×107m/s.

Conclusion:.

Velocity=1.9×107m/s

(b)

To determine

How long does it take the electron to travel the 1-cm distance? Compare the results to those of Problem 2.17.

(b)

Expert Solution
Check Mark

Explanation of Solution

Given info:.

V=1000Vd=0.01mm=9.11×1031kgq=1.602×1019Crb=20.22×103m=1.01×102mra=1×104m.

Formula used:.

Force

F = ma = qE

Calculation:.

We have force,

  F=ma=qEa=qEm.

For a cylindrical capacitor,

E=1rVln(rbra).

We have,

v=at=drdt=qmVrln(rbra)trdr=qmVln(rbra)tdtrarbrdr=qmVln(rbra)0ttdt12(rb2ra2)=qmVln(rbra)t22t=(rb2ra2)qmVln(rbra)=((1.01×102)2(1×104)2)1.602×10199.11×10311000ln(1.01×1021×104)=1.65×109s.

This value is higher than the value obtained in Problem 2.17

Conclusion:.

Time taken=1.65×109s

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