8.2. Magnetic Fields and Capacitance

• Capacitance is calculated as C = Q / V, where Q is the charge in the plates (C), V is the potential difference across the plates (V).
• The relative permittivity, also known as dielectric constant, is the ratio of the charge stored with the dielectric between the plates to the charge stored when the dielectric is not present.
• The greater the relative permittivity, the greater the capacitance of the capacitor.
• The area under the graph of charge against potential difference represents the energy stored by the capacitor.
• The discharging of a capacitor through a resistor is described by the Q against t graph.
• The charging of a capacitor through a fixed resistor is described by the Q against t graph.
• The time constant is the time it takes for the charge in a capacitor to fall to 37% of the initial value, given by RC (resistance x capacitance).
• A capacitor is considered fully discharged after 5 time constants.
• The electrons are deposited on plate A, making it negatively charged during the charging of a capacitor.
• Electrons travel from plate B to the positive terminal of the battery, giving the plate a positive charge during the charging of a capacitor.
• The time constant, RC, is derived by starting with the formula Q = Q 0 e -t/RC.
• P.d decreases exponentially across the plates during the discharging of a capacitor.
• Charge on one plate A decreases as it loses electrons, and plate B gains electrons, neutralising them during the discharging of a capacitor.
• Electrons build up on plate A and an equal amount of electrons are removed from plate B, creating a potential difference across the plates during the charging of a capacitor.
• When the p.d across plates = source p.d., the capacitor is fully charged and current stops flowing during the charging of a capacitor.
• The time taken for a capacitor to charge or discharge is affected by the capacitance of the capacitor, C, and the resistance of the circuit, R.
• The half time of a capacitor, T½ = 0.69RC, is a constant.
• Charging up a capacitor produces Q = Q 0 (1 - e -t/RC) and V = V 0 (1 - e -t/RC), where V 0 is the battery PD and Q 0 =CV 0.
• Electrons move from negative to positive around the circuit during the charging of a capacitor.
• The three expressions for the energy stored by a capacitor are E = ½ (Q 2 /C), E = ½ (QV), and E = ½ (CV 2 ).
• During the discharging of a capacitor, electrons move in the opposite direction than when the capacitor was charging up.
• When a magnetic field is perpendicular to a current-carrying wire, the wire feels a force, with the magnitude of the force equal to the product of the magnetic flux density (B), the length of the wire (L), and the current in the wire (I).
• Each Dee is a metal electrodes with opposite charges, this creates an electric field in the gap between the two Dees.
• The magnetic field causes the particles to move in a circular motion, which allows it to gain speed whilst minimising space.
• As they speed up the radius of their motion increases, until it breaks free tangential to one of the Dees.
• Fleming's left hand rule for motors represents the properties of a magnetic field as the thumb, first finger, and second finger.
• Magnetic flux density (B) is the flux per metre² and is measured in Tesla (T) or Webers/meters² (Wb/m²).
• A charged particle moving through a field feels a force when it is traveling along the field lines or perpendicular to them.
• Transformer efficiency is the ratio of output power in the transformer to input power, represented as IsVs / IpVp.
• A primary coil wrapped around an iron core with an alternating p.d creates an alternating magnetic field, which induces an EMF in a secondary coil also wrapped around the core.
• The number of coils in a transformer is linked by the equation Ns / Np = Vs / Vp.
• The EMF induced in the secondary coil creates a current.
• Transformers are used to increase the voltage and reduce current when transporting power, with minimal energy loses.
• In a step-up transformer, the secondary coil has more coils as it increases the voltage.
• Eddy current losses can be reduced by using a laminated iron core.
• Eddy currents are induced within the iron core as the primary coil’s magnetic field induces an EMF in the secondary coil.
• Eddy currents are a problem as they reduce efficiency by causing energy loss via resistive heating of the iron core.
• The equation for the Force felt by a moving charge in a magnetic field is F = BQv.
• The force applied to the particles is applied perpendicular to the particles motion, causing it to move in a circular motion.
• Cyclotrons use both an electric field and a magnetic field.