Electromagnetism Test. 5

The soft iron core concentrates the magnetic field lines, making the field stronger. When shaped cylindrically, it also ensures the field is radial, meaning the torque is proportional to the current for a wider range of deflection.

In a uniform magnetic field, the forces on opposite sides of the loop are equal in magnitude and opposite in direction, so they cancel out, resulting in zero net force.

The electron beam strikes a fluorescent screen, causing a single point to glow. This spot is then moved around by deflection plates to trace out a waveform.

This energy loss is represented by the area of the material's hysteresis loop. It is the energy required to re-orient the magnetic domains in the core with each AC cycle.

The energy stored is given by E = 1/2 LI². If I is doubled, the energy becomes 1/2 L(2I)² = 4(1/2 LI²), which is four times the original energy.

The induced EMF in a generator is given by E = NBAωsin(ωt). Since angular frequency ω = 2πf, the maximum EMF (E_max = NBAω) is directly proportional to the frequency. Doubling the frequency doubles the maximum EMF.

A steady DC current creates a constant magnetic field and thus a constant magnetic flux. Transformers require a *changing* magnetic flux to induce a voltage in the secondary coil, according to Faraday's Law.

The right-hand grip rule shows that the magnetic field lines form circles in a plane perpendicular to the wire.

Using F = qvBsin(θ), with sin(90°)=1. F = (2 x 10⁻⁶ C) * (3 x 10⁶ m/s) * (0.5 T) = 3.0 N.

For the net force to be zero, the electric force (FE = qE) and the magnetic force (FB = qvB) must be equal in magnitude and point in opposite directions, so they cancel out.

From the force equation on a wire, F=ILB, we can rearrange to B=F/IL. The units are Newtons / (Amperes * meters).

Paramagnetic materials have unpaired electrons that align with an external magnetic field, causing a weak attraction.

An AC generator uses slip rings to maintain a continuous connection, producing an alternating current. A DC generator uses a split-ring commutator to reverse the connection every half turn, producing a direct current.

A metal detector uses a coil to generate a changing magnetic field. When a metal object is nearby, this field induces eddy currents in the metal. These currents, in turn, generate their own magnetic field that is detected by a second coil in the detector.

Using E = BLv. E = (0.2 T) * (0.5 m) * (4 m/s) = 0.4 V.

This is the definition of mutual induction, the principle behind transformers.

Faraday's Law of Induction, E = -N (dΦ/dt), directly relates the rate of change of magnetic flux to the induced EMF. For N=1, a rate of 1 Wb/s produces 1 V.

The torque is given by τ = NIABsin(θ), where θ is the angle between the field and the normal. If θ = 0 degrees, sin(0 degrees)=0, so the torque is zero. The forces are pulling outwards, not causing rotation.

The output voltage of an ideal transformer depends on the turns ratio and the input voltage, not the frequency.

For an ideal transformer, input power equals output power (VpIp = VsIs). So, Ip = (VsIs) / Vp = (12 V * 2.0 A) / 240 V = 0.1 A.