Electric and Magnetic Field

Name	Definition	Formulae	Notes
ELECTROSTATICS
Radial field
Coulomb’s Law	Forces between two charges obey an inverse	$F=frac{kQq}{r^{2}}$ $k=frac{1}{4Pi varepsilon_{o}}$ $=8.9times 10^{9}$
Electric field	A region where a charged particle experience a force
Electric field strength	The force per unit charge acting on a small positive charge	$E=frac{F}{Q}=frac{kQ}{r^{2}}$
Electrical Potential Energy	The work done against the electric field in moving the charge from infinity to that point in the field	$EPE=frac{kQq}{r}$
Electrical Potential	$V=frac{P}{I}=frac{E}{Q}$	$V=frac{kQ}{r}$
	$EA=frac{Q}{varepsilon _{o}}$
CAPACITOR
Uniform field	Field strength are equal at all point Arrows show the direction of a small (+) charges will move when placed in the electric field
Equipotential surface	The plates, always perpendicular to the electric field line
Electric field strength	d: distance from positive plate	$E=frac{V}{d}$
Capacitance	Charge stored per unit p.d	$C=frac{Q}{V}$ $=frac{Avarepsilon _{o}varepsilon _{r}}{d}$	$varepsilon_{r}$ : relative permittivity For air, $varepsilon_{r}$ = 1
.Capacitor	A device for storing charges
Energy stored by a capacitor	The area under the graph (triangle) $W=frac{1}{2}QV=QV_{average}$	$W=frac{1}{2}QV$ $=frac{1}{2}CV^{2}$ $=frac{Q^{2}}{2C}$
Time constant	Time taken for the charge to fall to 0.37 of its initial value	RC
Charging	Shape of graph (current) exponential decay, current decrease by equal fraction in equal time interval The cell pushes charges through the circuit A current flows, charges are added to the \|\| until =0 $V_{c}$ increases, $V_{R}$ decreases, decreases $varepsilon =IR+frac{Q}{C}$		$I=I_{o}efrac{-t}{RC}$ $lnI=lnI_{o}-frac{t}{RC}$
Discharging	Capacitor pushes charges (opposite direction) through the resistor from negative plate to positive plate A current flow, charges are removed exponentially till 0		$I=I_{o}efrac{-t}{RC}$ $lnI=lnI_{o}-frac{t}{RC}$

Changing AC to DC
Changing AC to DC	Smoothed DC, Exponential decay Capacitor store charges If RC > T of AC, the capacitor doesn’t fully discharge before being charged	Rectified circuit Current change direction (Charge battery: without diode charges and discharge)	Normal circuit
Microphone condenser	$C=frac{Avarepsilon _{o}}{d}$ So as d↑↓, C↑↓, Q↑↓, I↑↓ If $RC=frac{1}{f}$ , I vary with frequency f
Root mean square	$l_{rms}$ is equal to the direct current that give the same average power output $P^{-}=I_{rms}^{2}R$	$V_{rms}=frac{V_{o}}{sqrt{2}}$ $I_{rms}=frac{I_{o}}{sqrt{2}}$

Name	Definition	Formulae	Note
FLUX
Magnetic flux density	The force per unit length per unit current on a long straight wire perpendicular to the magnetic field lines	$B=frac{F}{IL}$ $frac{1}{sqrt{varepsilon _{0}I_{o}}}=c$
Flux	The B*(the area perpendicular to the field lines)		Unit: Wb
MAGNETIC FIELD
Magnetic field	The direction of magnetic field is the direction North pole of compass will point if placed in the field
Magnetic field around a wire	A moving charge create a magnetic field Field line are concentric circles The magnetic field gets weaker as the distance from the wire increase Right-hand grip rule tells the direction of the field All magnetic field are closed loops All magnetic field are created by a moving electrical charge Fleming’s left-hand rule give direction Two parallel wires carry current in the same direction attracts
CURRENT CARRYING CONDUCTOR
Equation
The dynamo effec	The coil will rotate Speed of the motor depend on B, I, N, Area of the coil The commutator ensures that the current always flow in the same direction around the loop so the loop rotate in the same direction. Magnetic flux goes from 0 to a maximum An alternating emf is produced
CHARGED PARTICLE BEAMS
Equation	F perpendicular to v, v is constant hence centripetal force
ELECTROMAGNETIC INDUCTION
Faraday’s Law	Magnitude of the induced emf is directly proportional to the rate of change of flux linkage	$varepsilon =frac{d(N_{Phi })}{dt}$	Flux change → induced emf
Lenz’s Law	The induced emf cause a current to flow as to oppose the change in flux linkage that creates it	$varepsilon =frac{-d(N_{Phi })}{dt}$	To create a current in the coil work must be done so there is a force → induce B field in the coil oppose the change in B field
Magnet & coil	As magnet move, there’s a change in flux Faraday’s law: induced emf proportional to the rate of change in flux Initial increase in emf as magnet get closer to the coil When magnet is fully inside the coil there is no change in flux so no emf Changing direction of magnet, direction of emf change Magnitude of emf depends on the speed of magnet Same total flux so the areas of two graphs are equal
	Work done by magnet: Lenz’s law, induced current creates a B field to oppose motion Hence force in opposite direction to its motion
	hence work is done
	Ways to create induced emf: Moving the magnet Changing the current (turn on off) Change into alternating current
TRANSFORMER

Transformer effect	An electrical machine for converting an input AC PD into a different output AC PD $N_{s}>N_{p}$ : Step up transformer $N_{s}<N_{p}$ : Step down transformer $frac{V_{s}}{V_{p}}=frac{N_{s}}{N_{p}}=frac{I_{s}}{I_{s}}$
Transformer effect	The changing I in the primary coil create an changing B field in the iron core There is a changing in flux linked to the second coil Faraday’s law $(varepsilon=frac{d(NPhi )}{dt} )$ there’s an induced emf Ideal transformer: No flux loss Since $frac{N_{s}}{N_{p}}<1$ Step down transformer so low emf across secondary coil
Energy loss	Ohmic losses	The primary and secondary coils get hot	Make wire resistances small so heating losses are small
	Flux losses	Not all the flux stays in the iron core	Use soft iron core so the flux linkage is as large as possible & hysteresis losses are as small as possible
	Hysteresis losses	Magnetising and demagnetising the core produce heat
	Eddy current	The changing flux in the iron core creates current in the core, which also generate heat, dissipate energy	Use laminated core, so the eddy current are as small as possible
Power plant