Electromagnetic Induction Test. 3

Using the formula ε = BvLsin(θ). Given B=0.4 T, v=5.0 m/s, L=2.0 m, and θ=30°. So, ε = (0.4)(5.0)(2.0)sin(30°) = (4.0)(0.5) = 2.0 V.

As the coil rotates through the magnetic field, the direction of the induced EMF and current reverses every half turn, which is the definition of alternating current.

An ideal transformer is a theoretical concept with no energy losses, meaning its output power equals its input power.

The formula for energy stored in an inductor is E = (1/2)LI² = (1/2)(1 H)(2 A)² = 2 J.

Soft iron effectively concentrates the magnetic flux lines, leading to a much stronger magnetic field and a more efficient device.

Transformers operate on the principle of mutual induction, which requires a *changing* magnetic flux to induce an EMF in the secondary coil. A steady DC current creates a constant magnetic flux.

Every real inductor is made of wire, which has some inherent electrical resistance (R) that opposes the flow of any current, DC or AC.

Laminating the core increases its overall resistance to the flow of eddy currents, thereby minimizing the energy dissipated as heat.

This is a statement of Gauss's law for magnetism. Since there are no magnetic monopoles, any magnetic field line that enters a closed surface must also exit it, making the net flux zero.

The frequency is the number of cycles per second. Doubling the rotational speed doubles the number of rotations completed each second, thus doubling the frequency.

When the conductor moves, the free charges inside it also move through the magnetic field. They experience a magnetic force (F=qvB) that pushes them to one end of the conductor, creating the potential difference.

A metal detector creates a changing magnetic field. When a metal object is near, eddy currents are induced in it. These currents create their own magnetic field that the detector picks up.

Resistance is a property that affects current flow and energy loss (heat), but it does not determine the geometric property of mutual inductance.

The negative sign mathematically signifies that the direction of the induced EMF is such that it creates a current whose magnetic field opposes the change in magnetic flux that produced it.

The formula for self-induced EMF is ε = -L(ΔI/Δt). The magnitude is |ε| = (2 H)(5 A/s) = 10 V.

At the moment it's switched on, the armature is not yet rotating, so its speed is zero. Since back EMF depends on the speed of rotation, the back EMF is initially zero.

When a conductor moves in a magnetic field, the induced eddy currents create a magnetic force that opposes the motion, causing a damping effect.

Power loss in transmission lines is due to heat (P = I²R). By stepping up the voltage, the current (I) is reduced for the same amount of power, which significantly minimizes the I²R losses.

This is the fundamental principle: the magnetic force on the wires of the coil creates a torque that causes rotation. This is the 'motor effect'.

For an ideal transformer, (Is/Ip) = (Np/Ns). So, Is = Ip x (Np/Ns) = 2 A x (10/1) = 20 A.