Electricity and Magnetism

properties of electrical charges

positive and negative, total charge within system are conserved, charge is a lorentz invariant- is not changed when moving relativistic speeds, only come in quantities of e

what did milikan’s oil drop experiment find

charge is quantised in e, oil droplets were charged, charge changed until weight = electric force

what is coulomb’s law

follows superposition principle

what is the triboelectric effect

rubbing touching objects can transfer electrons, causes static electricity and damages electrons

what is the voltage from the triboelectric effect

what is the induced charge like without a ground

charges are free to move, + attracted, - repelled

what are induced charges with ground like

charges free to move, if ground and negative removed, conductor stays charged

what is induced charge like with an insulator

charges not free to move, aligns dipoles

what is a field

quantity that has a value at all points in space and time in a system

what is an electric field equation

what are properties of electrostatic field lines

point towards negative, strength represented by density, never cross, follows superposition principle

work done on a parallel capacitor

charge feel force strenght qE, work done = Fd

what is the potential difference of a capacitor

what is the energy of a parallel capacitor

what is gauss’ law

properties of electric fields

are conservative, work done on moving charge is independent of route taken, by moving a charge energy is converted into potential energy to E-field

what is the work done in an e-field

work done for a closed loop

is a line integral

what is electric potential

voltage = potential energy per charge

what is scalar potential field

work done per charge is a field, energy has no direction, measured in volts (J/C)

what is the potential of a scalar

what is an equipotential surface

points in space that have the same electric potential, no work is done along an equipotential, E-fields are normal to them, larger density = stonger E-field

potential energy to electric field equation

what is a perfect conductor

no resistance, all points have the same electric potential so there is no potential difference, E-field = 0 , charge density = 0, all charge resides on surface

what is a capacitor

stores all charge when connected to a potential, measured in farads

how to calculate capacitance

what is a faraday cage

conducting enclosure, free charges in conductor rearrange so that E-field inside is 0 due to superposition cancelling

how does charge q in faraday cage affect it

at all points E-filed is 0 , flux is 0

charge enclosed induces -q at surface of cavity to keep it neutral

creates E-field in conductor, charge on outside of cavity is not uniform

how does charge in 1 cavity effected other cavity of faraday cage

does not induce any charge has no effects

what is the potential energy in a capacitor

what is a dipole (p)

formed from 2 equal and opposite charges that are separated by d and fixed to each other

how do dipoles act in insulators

when charge is brought near insulator, temporary dipoles are induced

what is the E-field on a line with dipole

what is the E-field perpendicular to dipole

what is the potential from a dipole

what is the general E-field of a dipole

differentiate potential

why dp dipoles have a torque and energy

no net force, has an angle so has a torque, force acts perpendicular at distance d/2, equilibrium at angle = 0, energy to bring dipole form infinity is at angle = pi/2

what is the total torque of a system

where p = qd

what is potential energy of a dipole

what is the unit for a magnetic field

tesla = N / (C ms^-1)

properties of magnetic field

charge moving through magnetic field experiences a force, force is perpendicular to motion and B-field

what is the force of a B-field

found using right hand rule, does no work

what is the lorentz force

what is the motion of a charge particle in a B-field

force is perpendicular to velocity, force from B-field = centripetal force

what is force on current carrying wire

BIL

what is the speed of curretn in wire

v = I / nAq

what is the worl done by a magnetic field

0

how do charges effect B and E-fields

B - is only non-zero if charge is moving

E - always non-zero

what directions do force in B and E-field act in

B - perpendicular to v and B

E - parallel to E

what is the Biot-Savart Law

I - current flowing through distance dl

dB - resulting magnetic field at point distance r in direction r

direction found through right hand rule

what is gauss’ law for magnetic fields

because flux form complete loops, have no magnetic monopoles

what is ampere’s law

j - current density vector

what are solenoids

helical coil of wire, N turns, length L, B-field in = uniform, B-field out = 0

what are mono/dipoles in magnetostatics

monopoles don’t exist, dipoles are ‘building blocks’

what is the vector magneitc moment

perpendicular to loop

what is the torque from dipoles in external B-fields

what is the potential from dipoles in external B-fields

what is ideal battery

work done to seperate charge

what is EMF

work done to overcome E-field in battery

what is the emf of a battery

total potential in volts in closed loop

what is potential of a motion in B-field

equation for flux of B-field

what is faraday’s law

changing flux provides emf, not always current

what is lenz’s law

direction of induced emf is in opposite direction to flux

what is emf created by rotating conducting disk

what is 4th maxwell equation

changing B-filed created E-field

what is an eddy current

current loops that exert a force, forces energy loss to heat

due to current not confined to wire, current oppose change in flux

fixed ampere’s law

equation for mutual inductance

M12 = M21

what is emf in transformer

how are number of turns and emf related in transformer

equation for mutual inductance of transformers