1.

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

Answer»

`(abcepsilon_0)/2`
`(acdepsilon_0)/2`
`(abdepsilon_0)/2`
none of these

Solution :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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