Electromagnetic Induction Test. 4

High inductance provides a large inductive reactance (X_L = 2πfL) to limit the current. Low resistance ensures minimal energy is wasted as heat.

Tesla is the unit of magnetic field strength. Tesla / Ampere is not a unit of inductance.

The driving torque on the armature is proportional to the magnetic field strength (B). A stronger field will produce a greater torque for the same current, leading to a higher rotational speed.

First, find the secondary RMS voltage: Vs = 200 V * (2500/500) = 1000 V. Then, find the peak voltage: V_peak = V_rms x sqrt(2) ≈ 1000 V x 1.414 = 1414 V.

From Faraday's law, ε = (ΔΦ/Δt), we can rearrange to get ΔΦ = ε * Δt. The units are therefore Volts multiplied by seconds.

Since the magnetic flux is Φ = B * A, even if the area A is constant, a change in the magnetic field strength B over time will cause a change in flux and induce an EMF.

Back EMF is a motional EMF and is directly proportional to the rotational speed of the armature. Therefore, it is at its maximum when the motor's speed is greatest.

From the formula ε_s = -M(ΔI_p/Δt), if (ΔI_p/Δt) = 1, then the magnitude |ε_s| = M.

Energy is required to re-align the magnetic domains in the core material with each cycle of the AC current. This energy is dissipated as heat and is known as hysteresis loss.

Rate of change of current: (ΔI/Δt) = (4 A - 2 A) / 0.1 s = 20 A/s. Then, |ε| = L(ΔI/Δt) = (5 H)(20 A/s) = 100 V.

A transformer requires a *changing* magnetic flux. A steady DC source creates a constant magnetic flux, so no induction occurs.

Soft iron is a 'soft' magnetic material with a narrow hysteresis loop. It is easily magnetized and demagnetized, which minimizes the energy lost per cycle.

Total energy is conserved and oscillates between being fully stored in the inductor's magnetic field and fully stored in the capacitor's electric field.

Electromagnetic induction requires a *change* in magnetic flux. If the field is constant and the loop is stationary, there is no change in flux.

According to Lenz's law, induced eddy currents create a magnetic force that opposes the motion (a braking force), so the net downward force is less than the gravitational force, and a < g.

Magnetic flux is given by Φ = BAcos(θ), where θ is the angle between the field and the normal. So, Φ = (2.0 T)(0.5 m²)cos(60°) = (1.0)(0.5) = 0.5 Wb.

Using Faraday's Law, |ε| = N |ΔΦ/Δt|. The change in flux ΔΦ = 8.0 Wb - 2.0 Wb = 6.0 Wb. So, |ε| = 100 * (6.0 Wb / 3.0 s) = 100 * 2 = 200 V.

In an inductor, the back EMF causes the current to reach its peak value a quarter of a cycle (90 degrees) after the voltage reaches its peak. We say the current lags the voltage.

Electromagnetic brakes work by inducing large eddy currents in a rotating metal disc. These currents create a magnetic field that opposes the rotation, producing a braking force.

The relationship between peak and RMS voltage is V_rms = V_peak / √2. So, V_rms = 340 V / 1.414 ≈ 240 V.