A circular coil of radius 10 cm , 500 turns and resistance 2Ω is placed with its plane perpendicular to the horizontal component of the earth's magnetic field. It is rotated about its vertical di

Question

A circular coil of radius 10 cm , 500 turns and resistance 2Ω is placed with its plane perpendicular to the horizontal component of the earth's magnetic field. It is rotated about its vertical diameter through 18 0 ∘ in 0.25 s . The current induced in the coil is (Horizontal component of the earth's magnetic field at that place is 3.0 × 1 0 − 5 T )

TestHub · Accepted Answer

Initial magnetic flux through the coil, ϕ i ​ ​ = B H ​ A cos θ = 3.0 × 1 0 − 5 × ( π × 1 0 − 2 ) × cos 0 ∘ = 3 π × 1 0 − 7 Wb ​ Final magnetic flux after the rotation ϕ f ​ ​ = 3.0 × 1 0 − 5 × ( π × 1 0 − 2 ) × cos 18 0 ∘ = − 3 π × 1 0 − 7 Wb ​ Induced emf, ε = − N d t d ϕ ​ = − t N ( ϕ f ​ − ϕ i ​ ) ​ ​ = − 0.25 500 ( − 3 π × 1 0 − 2 − 3 π × 1 0 − 7 ) ​ = 0.25 500 × ( 6 π × 1 0 − 7 ) ​ = 3.8 × 1 0 − 3 V I = R ε ​ = 2Ω 3.8 × 1 0 − 3 V ​ = 1.9 × 1 0 − 3 A ​

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