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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 ............

A

12.5

B

14.5

C

10

D

17

Text Solution

Verified by Experts

The correct Answer is:
A
`vec(A)= (pi R^(2))/(2) (hat(j) + hat(k))= (25)/(2) (hat(j) + hat(k)) m^(2)`
`phi= vec(B).vec(A) = (3hat(i) - 4hat(j) + 5hat(k)).(25)/(2) (hat(j) + hat(k)) Wb= (25)/(2) (-4 + 5)Wb = (25)/(2) Wb= 12.5Wb`
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