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Numerical · Q18

Q.A circular coil of 50 turns and area 0.20 m20.20\ \text{m}^2 is placed with its plane perpendicular to a uniform magnetic field of 0.4 T0.4\ \text{T}, so that the normal to the coil is parallel to the field.

(a) Calculate the magnetic flux linked with the coil.
(b) If the coil is now turned so that its normal makes an angle of 60∘60^\circ with the field, find the new flux linked with it.
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✓ Free question

Given: N=50N=50, A=0.20 m2A=0.20\ \text{m}^2, B=0.4 TB=0.4\ \text{T}.

(a) Plane perpendicular to BB (normal parallel to BB, θ=0∘\theta=0^\circ).

ΦB=NBAcos⁡θ=50×0.4×0.20×cos⁡0∘\Phi_B = NBA\cos\theta = 50\times0.4\times0.20\times\cos0^\circ

=50×0.4×0.20×1=4.0 Wb= 50\times0.4\times0.20\times1 = 4.0\ \text{Wb}

(b) Normal tilted to make 60∘60^\circ with the field.

ΦB=NBAcos⁡60∘=50×0.4×0.20×0.5\Phi_B = NBA\cos60^\circ = 50\times0.4\times0.20\times0.5

=4.0×0.5=2.0 Wb= 4.0\times0.5 = 2.0\ \text{Wb}

✓Final answer

  1. ΦB=4.0\Phi_B=4.0 Wb (maximum, normal parallel to field).
  2. ΦB=2.0\Phi_B=2.0 Wb after tilting the normal to 60∘60^\circ from the field.

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