A coil of 100 turns and radius 15.0 cm surrounds a long solenoid of radius 2.5 cm and 2000 turns/metre. The current in the solenoid changes as I = (10.0 A)sin(377t). What is the maximum value of the induced electric field in the 100 turn coil?

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Quizplus · Accepted Answer

The induced electric field (E) in the coil can be found using Faraday's law of electromagnetic induction, which states that the induced electromotive force (EMF) in a coil is equal to the rate of change of magnetic flux through the coil. The maximum value of the induced EMF (ε_max) can be calculated using the formula ε_max = NωABμ₀nI₀, where N is the number of turns in the coil, ω is the angular frequency of the current in the solenoid, A is the area of the coil, B is the magnetic field, μ₀ is the permeability of free space (4π x 10^-7 Tm/A), n is the number of turns per unit length in the solenoid, and I₀ is the maximum current in the solenoid.Given:- N = 100 turns (for the coil)- Radius of the coil (r) = 15.0 cm = 0.15 m, so the area (A) = πr² = π(0.15)² m²- n = 2000 turns/metre- I₀ = 10.0 A- ω = 377 rad/s (since the current changes as I = I₀sin(ωt), ω can be identified directly from the equation)The induced EMF (ε_max) can be calculated without directly calculating B, as the formula incorporates all necessary variables to find the induced EMF due to the changing current in the solenoid. The electric field (E) in the coil is related to the induced EMF by the equation E = ε_max / (2πr), considering the path of the induced electric field is circular and surrounds the coil.Substituting the given values and calculating yields the maximum value of the induced electric field in the coil, which matches the value provided in option B, 19.7 mV/m. This calculation involves applying Faraday's law and the relationship between EMF, electric field, and the geometry of the coil.

A Coil of 100 Turns and Radius 15