Electromagnetic Induction Test. 5

In an ideal transformer with 100% efficiency, the power input to the primary coil (Pp = Vp * Ip) is equal to the power output from the secondary coil (Ps = Vs * Is).

The formula for instantaneous EMF is ε = ε_max * sin(θ). So, ε = 170 V * sin(45°) = 170 V * (1/√2) ≈ 170 * 0.707 ≈ 120 V.

At the magnetic north pole, the Earth's magnetic field lines are directed vertically. As the plane flies horizontally, its wings do not 'cut' any vertical field lines, so the induced EMF is zero.

An induced EMF is produced by a *change* in magnetic flux. If a time-varying magnetic field is introduced, the flux will change from zero, and an EMF will be induced.

Using the transformer equation, Vs/Vp = Ns/Np. Vs = Vp * (Ns/Np) = 110 V * (1200 / 400) = 110 V * 3 = 330 V.

Each wire creates a magnetic field that is experienced by the other. Using the right-hand rules, the resulting forces pull the wires together.

The time constant represents the time it takes for the current to reach approximately 63% of its final value. It is defined as the ratio of the inductance to the resistance.

This is a direct consequence of Lenz's Law. The induced current creates a magnetic force that acts in the opposite direction to the velocity.

The RMS value for a sinusoidal waveform is the peak value divided by the square root of 2. V_rms = V_peak / sqrt(2) = 120 V / 1.414 ≈ 84.9 V.

As the metallic bob swings through the magnetic field, eddy currents are induced in it. These currents create a magnetic force that opposes the motion, causing the oscillations to be 'damped'.

The magnetic energy density is given by the formula u_B = B²/(2μ₀). It is proportional to the square of the magnetic field strength.

Using the transformer current relationship: Is = Ip x (Np/Ns) = 3 A x (200/50) = 12 A.

The time constant (τ) of an RL circuit is τ = L/R. Rearranging for R gives R = L/τ. First, L = 200 mH = 0.2 H. So, R = 0.2 H / 0.02 s = 10 Ω.

An induction coil uses a rapid interruption of current in the primary to cause a very fast collapse of magnetic flux, which induces a very high voltage pulse in the secondary coil.

This is an example of motional EMF. The moving charges in the liquid experience a Lorentz force that separates them, creating a voltage.

Slip rings provide a continuous electrical connection between the rotating armature and the stationary external circuit.

Using the formula |ε| = L |ΔI/Δt|. First, convert inductance L = 50 mH = 0.05 H. The change in current ΔI = 4 A - 0 A = 4 A. So, |ε| = 0.05 H * (4 A / 0.01 s) = 0.05 * 400 = 20 V.

This demonstrates that magnetic monopoles (isolated north or south poles) do not exist. Any piece of a magnet must have both a north and a south pole.

A GFCI uses a transformer to detect differences between the outgoing and incoming current. A difference creates a changing flux, inducing an EMF that trips the circuit.

This is Oersted's discovery. The current in the coil creates a magnetic field that interacts with the magnetic needle of the compass.