Electric Fields Year 13. Electrostatic force Like charges repel, unlike charges attract How does this force act if charges are not in contact? –An electric.

Electric Fields

Year 13

Electrostatic force

• Like charges repel, unlike charges attract

• How does this force act if charges are not in contact?– An electric field exists

Electric field lines

• An electric field is a region where a charged body experiences an electrostatic force

• Like gravitational fields, we can represent electric fields by field lines– Lines show the direction of the force experienced by a

positive test charge– Lines never cross– The more lines, the stronger the field– Lines start and stop at charges (or ∞)

• Experiment to see field patterns

Electric field patterns

Equipotentials

• Equipotentials join points in a field at the same potential– No work is done moving along equipotentials

• Equipotentials are perpendicular to field lines• Any conductor is an equipotential surface

– Because charge is free to spread out

(resourcefulphysics.org) TAP 406.3

Coulomb’s Law

• 0 is called the permittivity of free space.• Permittivity is a property of a material that is

indicative of how well it supports an electric field.• Different materials have different permittivities,

and so the value of k in Coulomb’s law will change for different materials.

Coulomb’s Law

• Inverse square law, like gravity

• Attractive (-) or repulsive (+) force

• Valid for point charges or charged spheres

221

r

qkqF

Worked example– k = 1/ (40) = 9.0 109 N m2 C-2

– mass of an electron = 9.11 10-31 kg– mass of a proton = 1.67 10-27 kg– G = 6.67 10-11 N m2 kg-2

•What is the force of repulsion between two electrons held one metre apart in a vacuum? •What is the gravitational force of attraction between them? •By what factor is the electric repulsion greater than the gravitational attraction?

•TAP 407.1

Electric field strength

• A property of the field, not the test charge

• Field strength is the Force felt by a unit charge

2r

kq

q

FE

Potential energy

• Zero electric potential energy defined at infinity

• Have to do work to bring a charge +q a distance r from a charge +Q

• Work is stored as electrical potential energy

• If two charges are opposite, it takes work to separate them, potential energy is negative.– Must keep track of signs!

+Q

Pr

+q

Infinity (∞)

r

kQqEPE

Electrical potential

• Potential is the potential energy per unit charge

– Units: J/C, or volts– A property of the field, not the charge

experiencing the field

• Field strength=-potential gradient

r

kQ

q

EPEV

dr

dVE

Potential around a positive chargePotential and electric field intensity E = - dV/dr

Potential (V)

Distance (x)

2 8 16416 4 28

High field intensity

Low field intensity

(resourcefulphysics.org)

Charged conducting sphere

• All charge resides on the outside of the sphere

• Electric field inside=0

• Potential inside is constant

Uniform electric field

• Found between two parallel plates– Equally spaced field lines– Equally spaced equipotentials

• F=EQ=ma– So a charge will experience

uniform acceleration from one plate towards the other

d

V

x

VE

d

Electron beam

cathode

+5 kV

anode

0 V

Accelerating charges

• Electrons experience a force

• Work done=QV (charge x pd between two points)=energy gained moving with field

• Found in electron guns (CRTs)

2

2

1aty

tvx x

:ntdisplaceme vertical

:ntdisplaceme horizontal

md

eV

m

Fa

0

2000

4000

6000

8000

10000

12000

14000

16000

0 20 40 60 80 100 120

Vx=3, ax=0, Vy(t=0)=0, ay=2.

Motion of a body under constant upward acceleration

Cathode Ray Tube (CRT)

Robert Millikan

Millikan’s oil drop experiment

Millikan’s Apparatus

Comparing electric and gravitational fields

Electric and gravitational fields• Similarities

– For point charges or masses, the variation of force with distance follows the inverse square law.

– Both exert a force from a distance, with no contact. – The field strength of both is defined in terms of force

per unit of the property of the object that causes the force (i.e. mass and charge).

• Differences– Gravitational fields can only produce forces of

attraction, whereas electric fields can produce attraction and repulsion.

– Objects can be shielded from an electric field, they cannot however be shielded from a gravitational field

– Electrostatic force is many orders of magnitude greater than gravitational force.