Figure 20.35 shows a thin, uni- formly charged disk of radius R. Imagine the disk divided into rings of varying radii r, as suggested in the figure. (a) Show that the area of such a ring is very nearly 2ar dr. (b) If the disk carries pos- itive surface charge density oơ, use the result of part (a) to write an expression for the charge dq on an infinitesimal ring. (c) Use the resu Example 20.6 to write the infinitesi
Figure 20.35 shows a thin, uni- formly charged disk of radius R. Imagine the disk divided into rings of varying radii r, as suggested in the figure. (a) Show that the area of such a ring is very nearly 2ar dr. (b) If the disk carries pos- itive surface charge density oơ, use the result of part (a) to write an expression for the charge dq on an infinitesimal ring. (c) Use the resu Example 20.6 to write the infinitesi
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Transcribed Image Text:73. Figure 20.35 shows a thin, uni-
formly charged disk of radius R.
Imagine the disk divided into rings
of varying radii r, as suggested
in the figure. (a) Show that the
area of such a ring is very nearly
2Tr dr. (b) If the disk carries pos-
itive surface charge density ơ, use
the result of part (a) to write an
expression for the charge dq on an
infinitesimal ring. (c) Use the result of (b) along with the result of
Example 20.6 to write the infinitesimal electric field dE of this ring at
any point on the disk axis, taken to be the x-axis. (d) Integrate over all
such rings to show that the net electric field on the axis has magnitude
CH
R
-dr
FIGURE 20.35 Problem 73
|x|
Vx + R².
E = 2mko
| 1
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