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A nonuniform electric field is directed along the x-axis at all points in space. This magnitude of
the field varies with x, but not with respect to y or z. The axis of a cylindrical surface, 0.80 m
long and 0.20 m in diameter, is aligned parallel to the x-axis. The electric fields E 1 and E 2, at
the ends of the cylindrical surface, have magnitudes of 2000 N/C and 1000 N/C respectively,
and are directed as shown. In Fig. 22.1, the charge enclosed by the cylindrical surface is closest
to:

A) 0.28 nC B) -0.60 nC C) 1.2 nC D) -1.2 nC E) -0.28 nC

Respuesta :

Answer:

E) -0.28 nC

Explanation:

For using Gauss law

we calculate flux through whole cylinder.

  • On curved part flux is zero
  • On left par flux is =[tex]-\pi *0.1^{2} 2000= -20*\pi[/tex]
  • On right par flux is =[tex]-\pi *0.1^{2} 1000= 10*\pi[/tex]

    Total flux =-10[tex]\pi[/tex]

According to Gauss law

net flux along closed surface=  [tex]\int\limits^a_b {E} \, ds=\frac{charge enclosed}{epsilon}[/tex][epsilon =8.85 *[tex]10^{-12}[/tex]]

 10[tex]\pi[/tex]=[tex]\frac{q enclosed}{epsilon}[/tex]

plug in the values

we get charge enclosed = -0.28 nC

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