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.