Answer:
1.57 V
Explanation:
The induced emf ε = -ΔΦ/Δt where Φ = magnetic flux = NABcosθ where N = number of turns of circular coil = 20, A = area of coil = πr² where r = radius of coil = 10.0 cm = 0.1 m , B = strength of magnetic field = 0.30 T,θ = angle between normal to are and magnetic field and Δt = change in time = 0.12 s
Now ΔΦ = change in magnetic flux through circular coil = Φ' - Φ
Φ = magnetic field when A is perpendicular to B , that is θ = 90°. So, Φ = NABcos90 = 0 and Φ' = magnetic field when A is parallel to B , that is θ = 0°. So, Φ' = NABcos0 = NAB
So, ΔФ = Ф' - Ф
= 0 - NAB
= -NAB
= -Nπr²B
= -20 × π(0.1 m)² × 0.30 T
= -0.19 Wb
So, ε = -ΔΦ/Δt
= -(-0.19 Wb)/0.12 s
= 1.57 Wb/s
= 1.57 V
The induced EMF in the coil is 1.57 V
The induced EMF is produced due to the changing magnetic flux through a coil. Mathematically EMF is the rate of change of flux.
E = -ΔФ/Δt
where ΔФ is the change in the magnetic flux, and
Δt is the time period
Initial magnetic flux through the coil is:
Ф = NABcosθ ,
N = 20, number of turns
A = area of the coil = πr² = 3.14 × (0.1)² = 0.0314 m²
B = 0.30 T, magnetic field
here θ = 90°
so , Ф = 0
Final magnetic flux through the coil is:
Ф' = NABcosθ, here θ = 0°, so
Ф' = 20 × 0.0314 × 0.30 × 1
Ф' = 0.1884 Wb
ΔФ = Ф - Ф'
ΔФ = -0.1884 Wb
given that Δt = 0.12s
E = -ΔФ/Δt
E = 0.1884 / 0.12
E = 1.57 V
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