Physics HL Y2 Electromagnetic Induction - Cezara

voltage across a capacitor

A capacitor charges and discharges *exponentially* V = Voltage across capacitor (V) V₀ = Initial voltage across capacitor (V) tau = time constant for capacitor - resistor combination t = time for which capacitor has been discharging (S)

Bainbridge mass spectrometer

A mass spectrometer allows the isotopic content of a sample to be measured. Ions of the same velocity but different mass will follow different circular paths when moving in a constant perpendicular magnetic field.

Bridge rectifier

A network of diodes that converts and a.c. signal into a d.c. signal.

Full-wave rectification

Altering an a.c. signal so that it is always positive. A *bridge rectifier* can be used for this.

Rectification

Altering an a.c. signal so that it only has positive components

induction

An e.m.f. is induced in a conductor whenever there is relative motion between the conductor and a magnetic field i.e. whenever magnetic lines of flux are cut. Induction also takes place whenever there is a time-changing magnetic flux passing through a coil of wire.

Diode

An electrical component that only allows current to flow in one direction

Discharge curve

An exponential curve that describes how V, I or q for a capacitor changes over time.

ideal transformer

An ideal transformer changes the voltage of an alternating current (AC) input without any loss of energy. If the output voltage (on the secondary) is greater than the input voltage (on the primary), it is known as a step-up transformer. If the output voltage (on the secondary) is less than the input voltage (on the primary), it is known as a step-down transformer. εp / εs = Np / Ns = Is / Ip εp,εs = Voltages across primary and secondary coils Np, Ns = Number of turns on primary and secondary coils Ip, Is = Current through primary and secondary coils

Dielectric

An insulator whose molecules can become *polarised* in an electric field. Used in capacitors increase the overall capacitance. Paper is often used as a dielectric in capacitors.

Capacitor Construction formula

C = ε A / d C = C = Capacitance in Farads (F) ε = Permittivity of free space (C² / N m²) A = Overlapping area of plates in square metres (m²) d = separation of plates in metres (m)

Energy stored in a capacitor

E = 1/2 C V² E = Energy stored in joules (J) C = capacitance in Farads (F) V = voltage across capacitor in Volts (V)

Faraday's Law

Faraday's law states that the magnitude of an induced e.m.f. is proportional to the rate of change of flux linkage. ε α (Δφ/Δt) ε is the induced e.m.f. in V Δφ is the change of magnetic flux in Wb Δt is the time taken in s

Faraday's law and Lenz's law

Faraday's law states that the magnitude of an induced e.m.f. is proportional to the rate of change of flux linkage. Lenz's law states that the direction of the induced e.m.f. is such that if an induced current were able to flow, it would oppose the change which caused it. Both laws are combined in the following relationship: ε = - N (Δφ/Δt) ε is the induced e.m.f. in V N is the number of turns of the coil Δφ is the change of magnetic flux in Wb Δt is the time taken in s The negative sign is Lenz's law

Fleming's Right Hand Rule

For Generators Used to determine direction of *conventional current* flow when a conductor is moved through a magnetic field.

magnetic flux linkage

For a coil of wire, if the amount of flux passing through one turn of a coil is φ then the total magnetic flux linkage with all N turns of the coil is Nφ. Its units are Wb.

Capacitors in Series

Increasing the number of capacitors *decreases* the overall capacitance.

Capacitors in Parallel

Increasing the number of capacitors *increases* the overall capacitance.

Lenz's Law

Lenz's law states that the direction of the induced e.m.f. is such that if an induced current were able to flow, it would oppose the change which caused it. For instance, if a magnet is pushed into a coil of wire the current induced in the coil creates a magnetic field which opposes the motion of the magnet.

Step down transformer

More coils on the *primary* than the *secondary*. Voltage in primary is higher than in the secondary.

Step up transformer

More coils on the *secondary* than the *primary*. Voltage in secondary is higher than in the primary

Half-wave rectification

Removing the negative component of an a.c. signal. A single *diode* can be used for this.

r.m.s voltage

Root Mean Square voltage Vrms = V₀ / √2 This is the d.c. equivalent voltage that will provide the same heating effect as the a.c voltage.

Smoothed a.c.

The addition of a capacitor to the rectification circuit smooths the signal making it more like true d.c.

Capacitance

The amount of charge stored per volt in a capacitor. C = q / V C = Capacitance in Farads (F) q = charge in Coloumbs (C) V = Voltage across plates in Volts (V)

rotating coil

The e.m.f. induced in a coil rotating within a uniform magnetic field is sinusoidal if the rotation is at constant speed. Changing the speed of rotation will change the maximum value of e.m.f. induced and the frequency of the alternating e.m.f.

resistance and power (peak and average) vs peak values

The equations relating resistance and power (peak and average) to peak values are as follows: R = V₀/I₀ = Vrms / Irms Pmax = I₀ V₀ Pav = ½ I₀ V₀ R is the resistance in Ω Pmax is the maximum power dissipation in the resistor in W Pav is the average power dissipation in the resistor in W Irms is the rms value of the current in A I₀ is the peak value of the current in A Vrms is the rms value of the voltage in V V₀ is the peak value of the voltage in V

magnetic flux

The magnetic flux passing through an area is defined as: φ = B A cos θ φ is the magnetic flux in Wb B is the magnetic field strength in T (Wb m⁻²) A is the area under consideration in m² θ is the angle between the magnetic field and the normal to the surface

Peak voltage

The maximum value of an a.c. voltage

root mean squared (r.m.s.) value

The r.m.s. value of an alternating current (or voltage) is that value of the direct current (or voltage) that dissipates power in a resistor at the same rate. The r.m.s. value is also known as the rating.

sinusoidal currents and voltages (peak and r.m.s.)

The relationship between peak and r.m.s. values for sinusoidal currents and voltages is given by the following relationships: Irms = I₀ / √2 Vrms = V₀ / √2 Irms is the r.m.s. value of the current in A I₀ is the peak value of the current in A Vrms is the r.m.s. value of the voltage in V V₀ is the peak value of the voltage in V

Time constant

symbol tau units: seconds (s) R = resistance in Ohms (Ω) C = Capacitance in Farads (F) This is the time taken for something (voltage, current, charge in a plate) to fall to 39.79% of its original value. A strange number? 39.79 = 1/e.

Permittivity of free space

symbol ε value 8.5 x 10E-12 C² / N m² Units C² / N m² or F/m This quantity effectively describes the ability of a vacuum to allow an electric field through.

e.m.f. induced in a straight conductor moving in a magnetic field

ε = B v l Where: ε = Induced e.m.f. (direction of e.m.f. given by Flemings Right Hand Rule) in Volts (V) B = Magnetic field strength in Tesla (T) v = velocity of conductor perpendicular to the magnetic field in metres per second (m s⁻¹) L = Length of conductor perpendicular to magnetic field in metres (m)