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Electric fields
Chapter
2 1
Chapter
electric charge
A field is a set of values corresponding to a physical quantity
– either scalar or vector – that are associated with every point in a space.
An electric
field
surrounds
every
charge.
The electric field vector is defined as the force on a point
charge q due to any other charges,when placed at any point in
space, divided by the charge q:
The set of values of wind velocity in a region is
one example of a vector field.
r
r F
E
q
The magnitude
of theelectric field
has units
of force/charge:
newton/coulomb
(N/C).
fields lines
The electric field can be represented by field lines.
By convention, these lines start on a positive charge and end on a negative charge.
Electric dipole: two equal
charges, opposite in sign.
The direction of the electric field
at any point is tangential
to the field line
through that point.
The magnitude of the electric
field is given by the density of
the fields lines.
The number
of field lines
starting
(ending)
on a positive
(negative)
charge
is proportional
to the magnitude
of the charge.
The electric field
is stronger where
field lines
are closer
together.
electric field of a point charge
A point charge is a non-dimensional particle with a non-zero charge.
A point charge Q in space determines the presence of an electric field,
which can be revealed using a test charge q.
Applying Coulomb’s law and the definition of an electric field
it is possible to calculate the magnitude of E:
kqQ
2
F
E  r
q
q
E
1 Q
4 0 r 2
or, interms of ε0, the vacuum permittivity (k = 1/4πε0):

E

1 Q
4 0 r 2
Force
on a point charge in an
electric field:.
electric field of a uniformly charged infinite plane
The electric field due to an infinite plane with
charge density σ is.
r

E
20
It is independent of distance from the plane.

Consider an electric field
between two large
parallel plates,
which are very thin
and are separated by a
distance d,
which is small
compared with plate
height and width.
One plate carries
a uniform surface
charge density σ
and the other carries a uniform
surface charge density –σ.
The total electric field at any point in space
is given by the vector sum of each electric field.
electric fields and conductors
The static (stationary
charge) electric field
inside a conductor
is zero. If it were not,
any charges would
move.
The net charge on a conductor resides
on its outer surface.
The electric field is perpendicular to the
surface of a conductor, otherwise
charges would move.
A neutral hollow metal box is placed
between two parallel charged plates as
shown. What is the field like inside the box?
The field inside the box is zero.
This is the reason why it can be relatively
safe to be inside an automobile
during an electrical storm.
motion of a charged particle in an field
The force on an object carrying charge q in an electric field is given by:
F = qE.
Therefore, if we know the mass and charge of a particle,
we can describe its subsequent motion in an electric field.
Problem
An electron (mass m = 9.11 × 10–31 kg) is accelerated in a uniform
field (E = 2.0 × 104 N/C) between two parallel charged plates.
The separation of the plates is d = 1.5 cm.
The electron is accelerated from rest, near the negative plate, and
passes through a tiny aperture in the positive plate.
• With what speed does it exit the aperture?
Solution:
F  ma  a 
v  2ad

F qE

 3.5  1015m/s2
m m
 v  1.0  107 m/s
electric potential energy and electric potential
The electrostatic force is conservative, i.e. the work done to move a charge from
one point to another does not depend on the path. A potential energy and a potential can be
defined for a conservative force.
Electric potential energy
The electric potential energy
of a particle is defined
as the negative work done
on a positive charged particle
in moving it
from a point a to a point b:
Electric potential
Electric potential is defined
as potential energy per unit
charge:
Va 
Ua
q
Ub Ua  W  qEd


Electric potential energy
is a property of the particle.
Electric potential is a
property of the space
where an electric field
is present. It is defined
at a point.
The unit of electric potential energy is the joule (J).
The unit of electric potential is the joule/coulomb = volt (V).
electric potential energy and electric potential
Only changes in potential can be measured, allowing the free assignment of V = 0:
Vba  V  Vb Va 
Ub  Ua Wba

q
q

Analogy between gravitational and electric potential energy
Two rocks are
at the same height,
they are at the same
potential.
The larger rock
has more
potential energy.
The two charges have
the same electric
potential, they are at
the same point in the
space. The charge 2q,
however, has more
potential energy.
electric potential and equipotential surface
The electric potential due to a point charge q at a distance r from the charge
is given by:

V r 
An equipotential surface is the
locus of all points where
the electric potential has
the same value: at every
point, it is perpendicular to
the electric field lines.
1 q
4 0 r

The work done
by the electric field
on a charged particle moving
along an equipotential
surface is zero → ΔV = 0.
Relationship between electric potential and electric field
V  Ed
d
