D2 electric and magnetic fields

conservation of electric charge

charges cannot be created nor destroyed, can be transferred from one body to another

charged particles are particles that

• carry electric charges

• and hence produce electric fields

• proton/electron have equal amount of charge, opposite polarity

methods of transferring electric charge

1. friction

2. electromagnetic induction

3. contact

4. earthing

charging by friction

• When two non-conductors are rubbed together, electrons can be transferred from one material to the other.

• One material ends up with more electrons (negative charge), and the other with fewer electrons (positive charge) → charge of equal magnitude but opposite polarity

charging by electromagnetic induction

• negatively charged rod brought near (but not touching) a metal conductor that is initially electrically neutral

• free-moving electrons in metal undergo redistribution of charges due to induction effect

• near end has more positive charge than negative

• far end has more negative charge than positive

• sphere is grounded, electrons transferred to earth

• ground connection broken and negative rod removed, sphere will have positive charge

charging by contact (gold leaf electroscope)

• The electroscope is neutral — its leaves hang straight down

• charged rod put on the metal disc of the electroscope.

• Since the metal is a conductor, electrons can move: some electrons from charged rod flow onto the surface of the electroscope and then to the leaves

• leaves become negatively charged, repel each other, rises away from plate

• the bigger the charge the more the leaf rises

charging by earthing

• positively charged rod brought near neutral conductor Q on insulating stand

• electrons on conductor Q attracted to positively charged rod P

• earthing by touch: electrons flow from earth to neutralise positive charge at opposite side of conductor Q

after breaking contact with conductor (ie stop touching), remove positively charged rod. resulting conductor Q is negatively charged due to excess electrons.

electric charge is quantised

charge exists as discrete units of elementary charge e = 1.6 × 10^-19

proof: millikan’s oil drop experiment

• fine mist of oil drops sprayed into chamber

• passed through nozzle and ionised by x-rays (added/removed electrons)

1. when E-field switched off (no potential difference across the two plates):

• oil drops fall under gravity

• reach terminal velocity v when drag force = gravitational force

2. when E-field switched on (potential difference applied across the two plates)

• some oil drops become stationary (no drag force) or rise upwards with new terminal velocity v’

• balance of forces enabled charge on individual oil drops to be determined

• charges found to have common factor 1.6×10^-19 C

note: charge is a scalar quantity even though it has +/-

electric field

• region of space where stationary charge experiences a force

• direction of electric field: direction in which a positive charge would move if it were free to do so

electric field patterns for single point charge

electric field patterns for single spherical conducting body

• no potential gradient across conductor (since charges free to move in conductor, would redistribute)

• therefore no electric field

• electric field of conductor is zero therefore field within charged conductor is zero.

• entire interior of conductor has same potential as the surface

• all charges are on the surface, not inside the conductor → potential difference is 0

electric field patterns between 2 point charges

electric field patterns between parallel charged plates

• equally spaced lines → uniform, regardless of the charged particle’s distance from either plate

• magnitude E of electric field strength is uniform E = V / d (units: V m^-1, this formula only applies to parallel plates)

  • V is potential difference between plates (magnitude only, no sign

  • d is perpendicular distance between the plates

• from positive to negative, since potential decreasing

coulomb’s law

the magnitude of the force between two point charges is directly proportional to the product of the magnitude of the charges and inversely proportional to the square of their separation

F=k Qq/r²

assumptions

• point charges

• separation of the two spheres is large compared to radii, so take as if charges concentrated at centres

• equal and opposite force acting on each mass (even if masses are not equal)

electric field strength

(at a point in the electric field) is the electric force exerted per unit positive charge on a small stationary positive charge placed at that point

E = F/q = kQ/r² (units V m^-1)

• where F is the electric force

• q is the charge of the point charge

• where Q is the source charge creating the field

notes

• small: point charges separation

• stationary: if moving in a magnetic field, would have electromagnetic force FB)

• positive charge: same direction as electric field

magnetic field

region of space where a small magnet would experience a turning force

direction is the direction in which a north-seeking pole points

magnetic field pattern of straight current carrying conductor

• concentric circular magnetic field lines around the straight conductor, with increasing distance between field lines

• direction follows RHGR

magnetic field pattern of single turn coil

magnetic field pattern of solenoid