Two closed circular conductors lie in the same plane. With the same change in the induction

| January 15, 2021 | education

Two closed circular conductors lie in the same plane. With the same change in the induction of a uniform magnetic field, an EMF of induction of 0.15 V appeared in the first, and 0.6 V. How many times is the length of the second conductor greater than the first?

EMF1 = 0.15 V.
EMF2 = 0.6 V.
L2 / L1 -?
According to Faraday’s law of electromagnetic induction, the electromotive force of the EMF induction is directly proportional to the rate of change in the magnetic flux ΔF: EMF = ΔF / Δt.
The magnetic flux Ф is determined by the formula: Ф = В * S * cosα, where В is the magnetic induction of the field, S is the area of ​​the frame contour, ∠α is the angle between the normal to the plane of the frame and the vector of magnetic induction.
Since the area of ​​the frame and its orientation in the field does not change, the formula will take the form: EMF = Δ (B * S * cosα) / Δt = S * cosα * ΔВ / Δt
Since the frame has the shape of a circle, its area S is expressed by the formula: S = P * R2, where P is the number pi, R is the radius of the frame.
EMF = P * R2 * cosα * ΔВ / Δt.
R2 = EMF * Δt / P * cosα * ΔV.
R = √ (EMF * Δt / P * cosα * ΔV).
We express the length of the circle L by the formula: L = 2 * P * R = 2 * P * √ (EMF * Δt / P * cosα * ΔВ).
L1 = 2 * P * √ (EMF1 * Δt / P * cosα * ΔV).
L2 = 2 * P * √ (EMF2 * Δt / P * cosα * ΔV).
L2 / L1 = 2 * P * √ (EMF2 * Δt / P * cosα * ΔV) / 2 * P * √ (EMF1 * Δt / P * cosα * ΔV) = √EMF2 / √EMF1.
L2 / L1 = √0.6V / √0.15V = 2.
Answer: the length of the second conductor is 2 times the length of the first one: L2 / L1 = 2.



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