Answer:
E = 1.98*10^-4 V
Explanation:
Area = 6.8mm² = 6.8*10^-6m²
Turns = 854N/mm = 85400N/m
I = 1.28A
w = 212 rad/s
From Faraday's law of induction, the induced EMF = -dΦᵦ / dt
where Φᵦ = magnetic flux through the loop and its given by Φᵦ = BA
B = μ₀ni is the field produced by the solenoid and A is the area of the loop.
B = 4π*10⁻⁷ * 85400 * 1.28*sin(212t)
B = 0.1373 * sin(212t)
Φᵦ = B*A = 0.1373 * 6.8*10^-6 * sin(212t)
Φᵦ = 9.3364*10^-7 * sin212t
The induce EMF E = -dΦᵦ / dt = -(9.3364*10^-7) * d(sin212t) / dt
After differentiating, sin212t = cos212
E = -(1.98*10⁴) cos 212t
The magnitude of the induced EMF |E| = 1.98*10^-4 V
