Transcript Electric Fields - the SASPhysics.com

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
• e0 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
kq1q2
F 2
r
• Inverse square law, like gravity
• Attractive (-) or repulsive (+) force
• Valid for point charges or charged spheres
Worked example
–
–
–
–
k = 1/ (4pe0) = 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
F kq
E  2
q r
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
r
P
+q
Infinity (∞)
kQq
EPE 
r
Electrical potential
• Potential is the potential energy per unit
charge
EPE kQ
V

q
r
– Units: J/C, or volts
– A property of the field, not the charge
experiencing the field
dV
• Field strength=-potential gradient E  
dr
Potential around a positive charge
Potential and electric field intensity
E = - dV/dr
Potential
(V)
High field intensity
Low field intensity
16
8
4
2
2
4
8
(resourcefulphysics.org)
16
Distance (x)
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
V V
E

x d
d
Accelerating charges
0V
cathode
+5 kV
anode
Electron beam
• Electrons experience a force
• Work done=QV (charge x pd between two
points)=energy gained moving with field
• Found in electron guns (CRTs)
horizontal displacement : x  vxt
1 2
vertical displacement : y  at
2
F eV
a 
m md
Motion of a body under constant upward acceleration
16000
14000
12000
10000
8000
6000
4000
2000
0
0
20
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60
80
Vx=3, ax=0, Vy(t=0)=0, ay=2.
100
120
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.