Figure shows five lettered regions in which a uniform magnetic field extends directly either out of the page (as in region `a`) or into he page. The field is increasing in magnitude at the same steady rate in all five regions, the regions are identical in area. Also shows are four numbered paths along which `oint vec(E). vec(dl)` has the magnitudes given below in terms of a quantity mag. Determine whether the magnetic fields in regions `b` through `e` are directed into ot out of the page.
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`|{:("Path",1,2,3,4),(oint vec(E).vec(dl),mag,2(mag),3(mag),0):}|`

Explanation

`oint_(1) vec(E)* vec(dl) = mag`
`oint_(3) vec(E)* vec(dl) =3(mag)`
It means field in `b` and `c` should be out of the page.
`oint_(4) vec(E)* vec(dl) = 0`
It means field in `e` will be opposite to that in c,i.,e., into the page. Similarly field into `d` is also into the page.