A circular coil of radius 10 cm , 500 turns and resistance 2 Ω is placed with its plane perpendicular to the horizontal component of the earth's magnetic field. It is rotated about its vertical diameter through 180° in 0.25 s (Horizontal component of the earth's magnetic field at place is 3.0 × 10-5 T ). Estimate the induced current in the coil.

Question

A circular coil of radius 10 cm , 500 turns and resistance 2 Ω is placed with its plane perpendicular to the horizontal component of the earth's magnetic field. It is rotated about its vertical diameter through 180° in 0.25 s (Horizontal component of the earth's magnetic field at place is 3.0 × 10-5 T ). Estimate the induced current in the coil. (A) 1.2 × 10-3 A (B) 1.9 × 10-3 A (C) 2.3 × 10-3 A (D) 2.8 × 10-3 A

Tardigrade Admin · Accepted Answer

φB text (initial) =B A cos θ=(3 × 10-5)(π × 10-2) cos 0° =3 π × 10-7 Wb flux after rotation, φB( text final )=(3 × 10-5)(π × 10-2) cos 180° =-3 π × 10-7 Wb Estimated value ε=N|(Δ φ/Δ t)| =(500 × 6 π × 10-7/0.25) =3.8 × 10-3 V I=(ε/R) =(3.8 × 10-3/2) =1.9 × 10-3 A

$1.2 \times 1 0^{- 3} A$

$1.9 \times 1 0^{- 3} A$

$2.3 \times 1 0^{- 3} A$

$2.8 \times 1 0^{- 3} A$

1.2×10−3A

1.9×10−3A

2.3×10−3A

2.8×10−3A

ϕB (initial) ​=BAcosθ=(3×10−5)(π×10−2)cos0∘ =3π×10−7Wb flux after rotation, ϕB( final )​=(3×10−5)(π×10−2)cos180∘ =−3π×10−7Wb Estimated value ε=N∣∣​ΔtΔϕ​∣∣​ =0.25500×6π×10−7​ =3.8×10−3V I=Rε​ =23.8×10−3​ =1.9×10−3A

$1.2 \times 1 0^{- 3} A$

$1.9 \times 1 0^{- 3} A$

$2.3 \times 1 0^{- 3} A$

$2.8 \times 1 0^{- 3} A$