Question

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

Answer 1

E) -0.28 nC

Step-by-step explanation:

For using Gauss law

we calculate flux through whole cylinder.

• On curved part flux is zero
• On left par flux is =
  `-\pi *0.1^(2) 2000= -20*\pi`

• On right par flux is =
  `-\pi *0.1^(2) 1000= 10*\pi`

Total flux =-10
`\pi`

According to Gauss law

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

10
`\pi`=
`(q enclosed)/(epsilon)`

plug in the values

we get charge enclosed = -0.28 nC