First slide

Magnetic Flux

Question

A small loop of area of cross-section 10^-4 m² is lying concentrically and coplanar inside a bigger loop of radius 0.628 m. A current of 10 A is passed in the bigger loop. The smaller loop is rotated about its diameter with an angular velocity $ω$ . The magnetic flux linked with the small loop will be

NA

A

10^-9 sin $ω$ t
B

10^-9 cos $ω$ t
C

10^-10 sin $ω$ t
D

10^-10 cos $ω$ t

Solution

We know that $Φ = BAcos ωt$
$Here B = \frac{μ_{0} i}{2 r} ∴ Φ = \frac{μ_{0} i}{2 r} \times Acos ωt = \frac{(4 \times 3 \cdot 14 \times 10^{- 7}) 10}{2 \times 0 \cdot 628} \times 10^{- 4} \times \cos ωt = 10^{- 9} \cos ωt$

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