Electromagnetic induction summary

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Electromagnetic induction summary

Electromagnetic Induction

Induced Voltage: When a conductor is in relative motion with a magnetic field, B, there is a force, F, on electrons in the conductor perpendicular to that magnetic field. As the electrons move in one direction there is a separation of electric charge, Dq, caused by the magnetic field. The resulting difference in electric charge at each end of the conductor produces an emf (‘electromotive force’: e). This emf is a voltage source, V = E/q, capable of causing a current, I=Dq/Dt, to flow in a circuit to which it is connected.

Induced Energy: The potential energy, E_P, that causes the relative motion, v, between the conductor, m, and the magnetic field, B, is transformed into the kinetic energy, E_k = ½mv², of that motion and electrical energy, E_E= Vq, of the emf, e. This is due to a second magnetic force, F, that opposes the original motion due to a second magnetic field, B, produced by the separating charges, I.

Electromagnetic Induction: When a conducting coil is in relative motion with a magnetic field (or stationary in a changing magnetic field), the resulting electric current in the coil is said to have been electromagnetically induced. When a conducting coil is connected to an emf source, the changing magnetic field produced around it can cause electromagnetic induction in a nearby second coil (but only while the current in the first coil is changing or the coil is moving relative to the second).

Magnetic Flux

Magnetic Flux: The amount of magnetic field passing through an area is called the magnetic flux, f, measured in Webers, ‘Wb’:

f = BAsinq,

B = magnetic field (strength) = [T = Teslas]

A = area being considered = [m²]

q = angle between the field and the area,

N.B. sin(90^o)= 1, sin(0^o)= 0, .: f_┴ = BA = f_max, f_║= 0 = f_min,

f = [W] = [Tm²], [T] = [Nm^-1A^-1]

.: f = [NmA^-1] = [JA^-1]

Because electromagnetic induction is caused by a relative change:

Df = DE/I,

DE = energy transformed into electrical energy, I = current carrying that electrical energy,

i.e., Magnetic Flux is the energy transformed per current induced.

Generating Electricity with an Induced EMF

Faraday’s Law: The average magnitude of emf, e_av, induced in a coil is equal to the rate of change of the magnetic flux, Df/Dt, passing through that coil:

e_av = Df/Dt, Df = f_f– f_i, & from above;

Df = DE/I, E = Vq, I = q/t,

.: Df = Vq/(q/t) = Vq*t/q = Vt = [Vs]

i.e., Change in Magnetic Flux is the emf induced in a time period.

Lenz’s Law: The amount of emf, e, induced in a coil is equal to the rate of change of the amount of magnetic flux, Df/Dt, passing through a number of loops, n, so that the magnetic field, B, that is produced by the current, I, caused by the emf, e, is in a direction that opposes, –, the direction of the change in flux:

e= –n Df/Dt, (N.B. use the right-hand grip to check this)

Generator: A Generator is a device in which a rotating coil in a magnetic field is used to induce an emf. A generating (output) coil is rotated inside a magnetic field produced by permanent magnets. It is therefore like an electric motor used in reverse!

Alternator: An Alternator is a device used to induce an emf. It differs from a generator in that the generating (output) coils are stationary (stator), while a supply (input) coil that is connected to a DC emf source is rotated (rotor) inside the output coil. This is safer because the slip rings are connected to the lower voltage supply coil rather than the higher voltage generating coil.

Describing an Alternating Current (AC)

Alternating Current: When an electrical current reverses direction (i.e., alternates) regularly and rapidly it is called an ‘alternating current’, AC. Generally, alternating currents are sinusoidal (i.e., a graph of its current over time is shaped like a sine wave). It can therefore be described by wave-like properties:

f: frequency = number of cycles per second (Hz).

T: period = time required for one cycle (s) = 1/f.

A: amplitude = magnitude from zero to maximum (peak).

p-p: peak-to-peak = magnitude from maximum to minimum.

rms: root mean square of values: x_rms =√(S (x_av–x)²),

V_rms = V_peak/√2,

I_rms = I_peak/√2,

P = IV, P = power, V= voltage, I = current:

P(V_rms) = P(V_DC): V_rms= V_DC ( for equivalent DC power).

P(I_rms) = P(I_DC): I_rms= I_DC (for equivalent DC power).

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