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In the given electric field vecE = [alph...

In the given electric field `vecE = [alpha(d+x)hati + E_0hatj] NC^(-1)`, where `alpha = 1NC^(-1)` hypothetical closed surface is taken as shown in figure .

The total charge enclosed within the close surface is

A

`(abcepsilon_0)/2`

B

`(acdepsilon_0)/2`

C

`(abdepsilon_0)/2`

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
A
a. `phi_(ABCD)=-acd` unit
`phi_(CDEF)=-beE_(0)` unit
`phi_(ABEF)=bcE_(0)+cint_(0)^(a)(d+x)dy`
`=+bcE_(0)+acd+cint_(o)^(b)xdx`
[Since `(x)/(b)+(y)/(a)=1` or `(dx)/(b)=(-dy)/(a)`]

`=[+bcE_(0)+acd+(acb)/(2)]` unit
Using Gauss's law, we get
`phi_(set)=(q_("in"))/(epsilon_(0))` or `q_("in")=(abcepsilon_(0))/(2)`
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