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A loop has two semi-circular arcs of ra...

A loop has two semi-circular arcs of radii `R (= (5)/(sqrtpi) m)` each in two mutually perpendicular planes xz & xy as shown in figure. A uniform & constant magnetic field `vecB = ( 3 hati - 4 hatj+ 5 hatk)T` exists in the region of the loop. Radius `R= (5)/(sqrtpi)m.` The quantity of magnetic flux through the loop ABCDA (in Wb) is ............

Text Solution

Verified by Experts

The correct Answer is:
`12.5`

`vecA = (pi R ^(2))/(2) (hat j + hatk) = 25/2 (hatj + hatk ) m^(2)`
`phi = vec B . vecA = (3 hati - 4 hatj + 5 hatk ). 25/2(hatj + hatk ) Wb = 25/2 (-4+5) Wb = 25/2 Wb =12.5 Wb`
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