A rod s in ritely krig with uniform near di rge density along its leri l, where

Question

A rod s in ritely krig with uniform near di rge density along its leri l, where > The rud es ln an xv plane and is para el t axis as shown n F 22.10.5. what is the sytrbalic express un or he electric field a the pont labeled in le figure, where the coordinates of point P are (a, b)? Give your answer in terms of i and coordinates/distances displayed in the figure. Also, give your answer in unit-vector notation. Enter a symbo the first box below and a unit vector in the second box. Note: You might hnduseful to refer to Interactive Exercises 22.9. There you will find the derivation tor the electric held produced by a uniformly charged rod of ninte length. ihe ds plic expression in Intinhcy-long red with unifonn incar charge densry > D 4y Interactive Figure 22.10.5: An infinitely long rd is parallel to the x axis. The field point P is at coordinates x = a, y = b. Fdit dit

Explanation / Answer

The total charge enclosed is qenc = L, the charge per unit length multiplied by the length of the line inside the cylinder.

Net flux = E A = E (2 r) L

By Gauss' Law the net flux = qenc/o

Therefore E (2 r) L = L/o

E = /[ 2 r o ]

Because k = 1/(4 o) this can also be written:

E = 2k/r

where r is distance from wire. From diagram, it can be seen r = D-b

E = 2k/(D-b)

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