A coil whose diameter is 0.40 m is in a variable magnetic field. As the magnetic induction of the field changes by 127.4 T during 2 s, an emf of 200 V is induced in the coil. Then the number of turns in the coil is approximately

Question

A coil whose diameter is 0.40 m is in a variable magnetic field. As the magnetic induction of the field changes by 127.4 T during 2 s, an emf of 200 V is induced in the coil. Then the number of turns in the coil is approximately (A) 20 (B) 25 (C) 30 (D) 50

Tardigrade Admin · Accepted Answer

φ=N B A |ε|=(Δ φ/Δ t)=N((π d2/4)) ⋅ (Δ B/Δ t) 200 V =N ⋅((π(0.4)2 m 2/4)) ⋅((127 ⋅ 4 T /2 s )) ⇒ N=24.98 ≈ 25

Q. A coil whose diameter is $0.40 m$ is in a variable magnetic field. As the magnetic induction of the field changes by $127.4 T$ during $2 s$ , an emf of $200 V$ is induced in the coil. Then the number of turns in the coil is approximately

$20$

$25$

$30$

$50$

$ϕ = NB A$
$∣ ε ∣ = \frac{Δ ϕ}{Δ t} = N (\frac{π d ^{2}}{4}) \cdot \frac{Δ B}{Δ t}$
$200 V = N \cdot (\frac{π ( 0.4 ) ^{2} m ^{2}}{4}) \cdot (\frac{127 \cdot 4 T}{2 s})$
$\Rightarrow N = 24.98 \approx 25$

Q. A coil whose diameter is 0.40m is in a variable magnetic field. As the magnetic induction of the field changes by 127.4T during 2s, an emf of 200V is induced in the coil. Then the number of turns in the coil is approximately

20

25

30

50