Electromagnetic Induction Test. 1

Magnetic flux is defined as Φ = BA cos(θ). Cosine is maximum (1) when the angle is 0 degrees, meaning the field is perpendicular to the surface.

One Weber is defined as the magnetic flux that, linking a circuit of one turn, would produce an EMF of 1 volt if it were reduced to zero at a uniform rate in 1 second.

When the coil is parallel to the field, its sides are moving perpendicularly across the field lines, cutting the flux at the maximum rate.

This is the fundamental principle describing how a changing magnetic field creates an electric field, inducing an electromotive force (EMF).

Inductance (L) is defined as the ratio of magnetic flux (Φ) to the current (I) that produces it, so L = Φ/I.

The rotating coil of the motor cuts its own magnetic field, inducing an EMF in itself that opposes the applied voltage. This is a classic example of self-induction.

Lenz's law dictates that the induced current creates a magnetic field that opposes the change, which requires work to be done, thus conserving energy.

This is the correct formula for motional EMF when the velocity, field, and length are mutually perpendicular.

The inductance of a solenoid is given by L = (μ₀N²A)/l. It is proportional to N².

From the energy formula E = (1/2)LI², we can solve for L: L = 2E / I². So, L = (2 * 25 J) / (10 A)² = 50 / 100 = 0.5 H.

The Right-Hand Palm Rule (or Fleming's Right-Hand Rule) is used for generators to determine the direction of the induced current (and thus EMF).

For an ideal transformer, Ip/Is = Ns/Np. Rearranging for Is gives Is = Ip * (Np/Ns). So, Is = 10 A * (100 / 2000) = 10 A / 20 = 0.5 A.

First convert 900 km/h to m/s: 900 x (1000/3600) = 250 m/s. Then, ε = BvL = (4.0 x 10⁻⁵)(250)(50) = 0.5 V.

According to Faraday's law, an induced EMF (and thus current) is generated only when the magnetic flux through the coil changes with time.

Using Faraday's Law, |ε| = N * A * |ΔB/Δt|. Here, ΔB/Δt = (10 T - 0 T) / 1 s = 10 T/s. So, |ε| = 50 * 0.02 m² * 10 T/s = 1 * 10 = 10 V.

Self-inductance opposes any change in the current flowing through the coil, similar to how inertia in mechanics opposes a change in the state of motion.

When moving parallel to the field lines, the conductor is not 'cutting' through any flux, so the change in flux is zero, resulting in zero induced EMF.

A transformer uses a changing current in a primary coil to induce a current in a magnetically linked secondary coil, which is the definition of mutual induction.

A generator, by definition, uses mechanical rotation (from a turbine, engine, etc.) to generate electrical power through electromagnetic induction.

Using the motional EMF formula ε = BvL. Given B = 0.5 T, v = 4 m/s, and L = 1.5 m. So, ε = (0.5 T)(4 m/s)(1.5 m) = 3.0 V.