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An electric field is uniform and in the ...

An electric field is uniform and in the positive x direction for positive x and uniform with the same magnitude but in the negative x direction for negative x. It is given that `E=200 hat(i) N//C` for `x gt 0` and `E=-200 hat(i) N//C` for `x lt 0`. A right circular cylinder of length 20 cm and radius 5 cm has its centre at the origin and its axis along the x-axis so that one face is at `x=+10` cm and the other is at `x=-10` cm
What is the net outward flux through each flat face?

Text Solution

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(a) `phi_(1)=vec(E).vec(A)=vec(E.).vec(A.)`
`=1.57" Nm"^(2)//C`
(b) `vec(E)` is parallel to sides of cylinder so `phi` through sides = 0
( c ) `phi =vec(E).vec(A)+vec(E.).vec(A.)=2EA`
`=2xx200xxpi(5xx10^(-2))^(2)"Nm"^(2)//C`
`=3.14" Nm"^(2)//C`
(d) `Q=phi epsilon_(0)`
`=3.14" Nm"^(2)//Cxx8.854xx10^(-12)" C"^(2)"N"^(-1)m^(2)`
`=2.78xx10^(-11)` C
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