A small loop is placed inside a solenoid. Solenoid has a varying current. The amplitude of the EMF induced in the loop is 2.7* 10⁻⁶ V.
Given that,
Area = 4.6 mm² = 4.6* 10⁻⁶ m²
Number of turns = 960 turns/cm = 96000 turns/m
Current I = 4.90 A
Angular frequency ω = 212 rad/s
From Faraday's law of induction, the induced EMF = -dΦ / dt
where Φ = magnetic flux through the loop and its given by Φ = BA
B = μ₀ni is the field produced by the solenoid
A is the area of the loop
B = 4π*10⁻⁷ * 96000 * 4.9 *sin(212 t)
B = 5911.2* 10⁻⁴ * sin(212 t) = 0.59 * sin(212 t)
Φ = B*A = 0.59 * 4.6* 10⁻⁶ * sin(212 t)
Φ = 2.7* 10⁻⁶ * sin(212 t)
The induce EMF E = -dΦ / dt = -(2.7* 10⁻⁶) * d(sin212t) / dt
After differentiating, sin212t becomes cos212t
E = -(2.7* 10⁻⁶) cos 212t
The magnitude of the induced EMF |E| = 2.7* 10⁻⁶ V
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