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Coulomb’s Law

The force between a charge q and another
charge Q a distance r apart is given by
qQ
FE  k 2
r

Where k = 9 x 109 Nm2/C2
Action-at-a-distance

Coulomb’s Law describes the force
between two charges. What happens
to the force on q if Q is suddenly
moved? How quickly does q realize the
change in force? What is it that q and
Q interact with?
Michael Faraday (1830s)



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
Faraday proposed the concept of the “Electric Field”
Charges create a “force field” surrounding themselves
Charge q would interact directly with the field created
by charge Q – it wouldn’t interact with Q directly
Charge Q would likewise interact with the field
created by q – not q directly
If Q were suddenly moved, q would still react to the
field that already exists in that region… The change
would move at the speed of light (the change in the
field actually IS light!)
Mapping a mine-field

Send disposable robots to
different points in the field – if
they blow up, put a marker at
that spot
BOOM!
Mapping an E-field

Place positive test charges at different
points in the field – measure the force
(magnitude and direction) acting on the
charge at that point
E-field around positive point charge
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E-field around
positive charge
points outward
Spacing of lines
represents
strength of field
Arrows point in
the direction of
the force that
would act on a
positive charge
placed in the field
E-field around negative point charge

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E-field around
negative charge
points inward
Spacing of lines
represents
strength of field
Arrows point in
the direction of
the force that
would act on a
positive charge
placed in the field
Definition of E-field

 F
E
q
E-field is measured in N/C
E-field around a point charge

Combine E = F/q
with Coulomb’s Law
to get
Q
Ek 2
r
E-field around a charge follows an inverse-square law
Field around multiple charges

Field around multiple charges is the
vector sum of the field at each point
around the charges
The electric field obeys a superposition principle. The
total field at any point is the vector sum of all fields at that
point.
E-field between parallel plates
The E-field between
two oppositely
charged plates is
uniform (constant)
 A charge placed
anywhere between
the plates will feel
the same magnitude
of force

E-field inside a conductor

When an E-field passes though a
conductor, charges will move around
until the E-field inside the conductor is
zero (an equilibrium is established)