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A loop made of straight edegs has six co...

A loop made of straight edegs has six corners at `A(0,0,0), B(L, O,0) C(L,L,0), D(0,L,0) E(0,L,L)` and `F(0,0,L)`. Where `L` is in meter. A magnetic field `B = B_(0)(hat(i) + hat(k))T` is present in the region. The flux passing through the loop `ABCDEFA` (in that order) is

A

`B_(0)L^(2)Wb`

B

`2B_(0)L^(2)Wb`

C

`sqrt(2)B_(0)L^(2)Wb`

D

`4B_(0)L^(2)Wb`

Text Solution

Verified by Experts

The correct Answer is:
B

Given, magnetic field
`vec B= B_(0)( hat i+ hat k)T`
Area vector of the loop will be the vector sum of two area vectors (area vector of loop ABCD and that of loop ADEF)
`therefore vecA= L^(2) hat k+ L^(2) hati= L^(2)(hat i+ hat k)m^(2)`
Magnetic flux through the loup ABCDEFA is
`phi- vec B. vecA= [B_(0)( hat i+ hat k)].[L^(2)(hat i+ hat k)]`
`= (B_(0)L^(2)+ B_(0)L^(2))= 2B_(0)L^(2)`
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