© John Parkinson

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Electric Field   

"An electric field is a region in which charged particles experience a force"

ELECTRIC FIELD

+Q FORCE-QFORCE

Lines of force show the direction of the force felt by a positive charge

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THE DENSITY OF THE FIELD LINES IS A MEASURE OF THE STRENGTH OF THE FIELD

-+

Field lines start and end on charges

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This is defined as the force per unit [+ve] charge acting at a point in the field.            

ELECTRIC FIELD

STRENGTH E

ELECTRIC FIELD STRENGTH E

Q

FE UNITS = ?N C-1

Hence the force on a charge of Q coulombs in the diagram above is given by :

+Q

F = E Q

IT IS A VECTOR

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Simply Potential [i.e. the volts] measures the energy of each coulomb of charge.

Electric potential, V

Electric potential is the electrical potential energy per unit charge (ie. per coulomb) at a point in a field.

This is the work done per unit charge in bringing a small positive charge from infinity to the point.

Potential only depends on the charge causing the field and is a scalar

Hence the energy of Q coulombs of charge at a point, where the potential is V

volts is given by W = QV

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+QA point charge or a

charged sphere produces a radial field

Lines of Equipotential V

These are perpendicular to the field lines

FIELD PATTERNS

At any point the field strength equals the potential gradient

r

VE

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+Q

Field & Potential due a point charge or charged sphere

At a distance r from the charge

204 r

QE

E is a

vector

r

QV

04 V is a

scalar

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FIELD PATTERNS Oppositely charged parallel plates produce

a uniform field between the plates

+++++++++++++++++++++++++++++

--------------------------------------------------

Evenly spaced equipotentials – so it’s a uniform field.

Equipotentials

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V Voltsd metres

The field is uniform

Hence the potential gradient V/r is uniform

Henced

VE

It follows that E has units of N C-1 or V m-1

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Electric Potential Contours (energy levels)

-Q +Q 0 V

-100 V

200 V

300 V

400 V

100 V

-200 V

-300 V

This is analogous to climbing

[and falling down]

gravity hills

QUESTION How much energy is required to move a +0.5 C charge from A to B?

A

B

The potential difference V = VB – VA = 200 – (- 100) = 300 Volts

W = Q V = 0.5 x 300 = 150 J

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Motion of Charge Initially Moving Perpendicularly to an Electric Field e.g. an electron in an oscilloscope beam.

- - - - - - - - - -

+ + + + + + + + + + +

Ex

y

--

vH

VH is the initial horizontal velocity and REMAINS CONSTANT - Like a projectile !!

For the vertical motion u = 0, som

Fa

2

2

1tay

For the horizontal motion, x = VH t

222x

mv

qEy

H

Hence which is a PARABOLA

where m = mass of the particle and F = EQ

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Gravitational Field Electric Field

Inverse Square Law Newton’s Law 2

21

r

MMGF

Inverse Square Law Coulomb’s Law 2

0

21

4 r

QQF

Field Strength g = force per unit mass & is a VECTOR

2r

Gmg

Field Strength E = force per unit charge & is a VECTOR

204 r

QE

Gravity Potential, Scalar & for Radial Field r

GMVg

Electric Potential ,Scalar & for Radial Field r

QV

04

Field strength = Potential Gradient

r

Vg g

Field strength = Potential Gradient

r

VE

Definition of potential Work done in bringing a unit mass from infinity to the point in the field

Definition of potential Work done in bringing a unit charge from infinity to the point in the field

Potential Energy gmV W Potential Energy QV W

Comparing Gravitational and Electric Fields