FIELDS

FIELDS

+Higher potential

Lower Potential

- Potential gradient = Electrical Field Strength

V

x

Electrical field

Gradient of slope = Vx Increases if V bigger

and x smaller

+ve charge moving towards –ve charge

+

- +

Field Strength Line patterns

-

+

(line to indicate direction of force felt by a +ve charge)

Uniform fieldNon-uniform fields

Field strength lines

Lines of equipotential – no work done on charge

Equipotential, 90 to field strength lines

Equipotentials in a uniform field will be equally

spaced

0V 800V

200V 400V 600V

Electric Force

• May be attractive (-ve) or repulsive (+ve)

• Force between two charges

Units = N

Symbol = F

Describing a uniform field

Electric Field Strength• Force per unit +ve charge

Symbol = E

Unit = N C-1

E = Fq

Important due to repulsive/attractive nature of force

Describing a uniform field

E = Vd

or V m-1

distance between charges (plates)

Electric Potential Energy• Energy of a +ve charged particle (q) due its position in an electric field

Units = C V = JSymbol = EPE

EPE = qV

Describing a uniform field

Acceleration due to electric field

10V

0V

+

EPE = qV

EPE = 0

+

potential energy = kinetic energy

qV = ½mv2

Important point:

K.E. gained is the same for both particles

Velocity is different due to difference in mass

Electron velocity quickly approaches the speed of light - relativistic.

Velocity equation only valid when v << c

The electron volt (eV)

A measure of energy

qV = ½mv2

1 eV = Energy gained when an electron is subjected to a potential difference of 1V

1 eV = 1.6 x 10-19C x 1V = 1.6 x 10-19 J

Millikan’s Oil Drop Experimentto measure charge on an electron

F (weight) = mg

F (electric attraction) = qE

mg = qE

Oil drop (charge q)

+

-

-

If the oil drop hovers then…

Forces experienced by oil drop?

The cunning bit...

Then ionise oil drop (using radioactive source)

Re-adjust the voltage (and therefore the size of E) to make oil drop hover again.

Change in voltage proportional to charge on an electron

Add or remove electrons

Kepler’s Laws

Kepler: Geometry rules the Universe

Sun

MarsAstronomy

Orbit of Mars an ellipse with Sun at a focus

Geometry

ab

focus focus

planet

Ellipse: curve such that sum of a and b is constant

Law 1: a planet moves in an ellipse with the Sun at one focus

Kepler 2Kepler: Geometry rules the Universe

Sun

MarsAstronomy

Speed of planet large near Sun, smaller away from Sun

Law 2: the line from the Sun to a planet sweeps out equal areas in equal times

Geometry

focus

planet

Areas swept out in same time are equal

slow

fast

Kepler 3Kepler: Geometry rules the Universe

Orbital period againstorbital radius

2

1

00 50 100 150 200 250

radius/million km

Orbital period squaredagainst orbital radiuscubed

4

2

00 1 3 4

1

3

2

Law 3: square of orbital time is proportional to cube of orbital radius

radius3/AU3

Mars

Mars

Earth

Venus

MercuryMercury

Venus

Earth

Apple and moon experimentby Newton

Acceleration of Moon towards EarthAcceleration of an apple towards Earth

Newton calculated...

Question - how does gravity extend into space?

Conclusion...

Angular acceleration of moon towards earth

(due to circular motion)=

Strength of earth’s gravity

at 60RE

Gravity changes at a rate of inverse square of distance

This extended gravitational force out into the universe - an amazing result (!)

Gravitational force, F

F = -Gm1m2

r2

F = gravitational force, NG = gravitational constant, 6.67 x 10-11 N m2 kg-2

m1 = mass of first object, kgm2 = mass of second object, kgr = distance between the two objects, m

Earth orbiting the sun

This is the gravitational force between the sun and earth

Requirement for an object to orbit

Fgravitational = Fcentripetal

Needed for circular motion

90 to velocity of object

N.B. m1 = mass at centre of orbit, m2 = mass of satellite

Gm1m2

r2= m2v2

r

Remembering v = 2rT

Gm1m2

r2= m242r

T2

T2 = 42r3

Gm1

(Kepler III)

Very important

The satellite must be travelling fast enough for its orbit radius (Kepler III)

• Not faster enough - orbit will collapse

• Too fast - will overcome gravitational forces and escape

Types of orbit

Geostationary

Polar

Relative to the earth it doesn’t move

T = 24 hours

Orbits N-S (over the poles), the earth rotates and so it looks at a different place each orbit.T = 90 minutes

If there is a force there is an acceleration

F = ma

If the force is due to gravitational forces then acceleration is acceleration due to gravity

F = mg

Gravitational field strength, g- better known as gravity

In words, gravitational force per unit mass acting at a point

Or g = Fm

Then

F = -GMmr2

r2

= -GMg = -GMmmr2

Know

units N kg-1

Gravitational Potential Energy = mgh

Stored ability to do work

Remember:

work = force x distance (in direction of force)

= mg x h

- something else has done work to get the object to that point

Uniform Field (near surface of Earth)

Change in GPE

mgh

mg(h + Δh)

mg(h + 2Δh)

mg(h + 3Δh)

Δh

h=0h

Forc

e (m

g) /N

Work done moving an object by Δh (near the earth’s surface, g constant)

Height /m

Δh

Area = mg Δh= work done

h1 h2

Gravitational potential

...“The work done to move unit mass from infinity to that point”...

Symbol = V

Unit = J kg-1

V = mgh = ghm

Don’t forget h r

Gravitational potential is the total work, against the gravitational force, for 1kg to go from a point where g = 0 to the point in question where g = x N kg-1.

g = 0 N kg-1 at r =

g = 9.8 N kg-1 at r = 6.4 x 106m

A convention...

GPE = 0

GPE = x

GPE = - x

GPE = 0

Space calculations

Earth only calculations

Work done moving an object from to r (Δr)

= m g drr

Area = work done

Δrr

Forc

e (m

g) /

N

r /m0

N.B. g isn’t constant (non-uniform field)

Gravitational potential - work done on unit mass i.e. m = 1kg

V = g drr

= GMr r

= - GM

r

V = - GM dr

r2r

Another interesting point...

V = g drr

Can be rearranged to ...

g = - dVdr

The gradient of gravitational potential is gravitational field strength.

Gravitational force F = - GMmr2

g = - GMr2

Gravitational field strength

V = - GMr

Gravitational potential

Energy conservation

Etotal = Ekinetic + Epotential

mgh = Etotal - ½mv2

gh = constant - ½v2

V -½v2

-½v2

r

V

r

The gradient of either graph is g

V = 0, r =

V = -62.5MJ kg-1

Energy required to get out of hole

Energy gained if falling into hole

Escape velocity

Stationary object (v = 0), at V = 0

½mv2 + mV = ETotal

Nudge object into well, ETotal = 0 K.E. increases as P.E. become more -ve

0 + 0 = 0

½mv2 + mV = 0v -2V V is -ve

At Earth’s surface V = -62.5MJ kg-1 , a

1kg mass will hit the ground at ~11km s-1

if nudged into well.

Conversely...

A 1kg mass launched at 11km s-1 will just make it to V = 0, the brim of the potential well.

11km s-1 = escape velocity