### Electric Fields

```Electric Fields
What is an Electric Field?
• An electric field is a region of space
surrounding a charged object.
• A stationary object experiences an electric
force in this region because of its charge.
• It extends outward through space.
• Every charge is surrounded by both a
gravitational and electric field.
Describing an Electric Field
• Electric fields have magnitude and direction.
• Electric fields are vector quantities.
• The magnitude of the field is determined by
the strength of the force that is acting on a
charge.
• E = F/q
• Force is measured in Newtons (N) and charge
is measured in Coulombs (C).
• Electric field strengths are measured in N/C
Sample Problem
• An electric field is measured using a positive
test charge of 5.0 x 10-6 C. This test charge
experiences a force of 2.0 x 10-4 N on it. What
is the magnitude of the electric field at the
location of the test charge?
• E = F/q
• E = 2.0 x 10-4 N/5.0 x 10-6 C
• E = 40. N/C
Describing an Electric Field
• What two variables contribute to the strength
of an electric field?
• Field strength increases as distance decreases
and as the magnitude of the charge increases.
• E = Kq/d2
• (q is the charge producing the field and d is
the distance from the charge)
Sample problem
• What is the magnitude of the electric field
strength at a position that is 1.2 m from a
point charge of 4.2 x 10-6 C?
• E = (9.0x109 )(4.2x10-6 )
(1.2)2
• E = 26000 N/C
Picturing an Electric Field
• The direction of the electric field is identified as the direction
the force would exert on a small POSITIVE test charge.
• Vector diagrams are used to represent electric fields.
• Not possible to show every vector so field lines, or lines of
force, are used to represent electric fields.
• Field lines point away from positive charges and toward
negative charges.
• Lines drawn far apart represent weak fields.
• Lines drawn close together represent strong fields.
Electric Fields and Conductors
• An electric field is equal to zero inside a
conductor.
• Excess charge resides on the surface.
• The electric field is perpendicular to the
surface.
• If irregularly shaped, charge accumulates
where the surface is smallest-for example at
sharp points.
Point to Ponder
• Is there a limit to how strong an electric field could
be?
• Yes there is a limit.
• The production of a field depends on a collection of
charges. After reaching a certain density, these
charges would begin to repel each other.
• Examples of electric field strength-field in a fluorescent tube- 10 N/C
-field produced by a lightning bolt-10,000 N/C
-field produced by an electron in a hydrogen atom51, 000 N/C
Energy and Electric Potential
• When charges move because of a force, work
is done.
• If work is done on a charge, potential energy is
gained. (For example; separating two unlike
charges, or moving two like charges together).
• If the work is done by the charge, potential
energy is lost. (For example; separating two
like charges, or moving two unlike charges
together).
Electric Potential Difference
• Electric potential difference (∆V) is defined as
the work done in moving a positive test
charge between two points in an electric field.
• ∆V = W/q
• (W is the work done on moving the charge; q
is the magnitude of the charge being moved).
• ∆V is measured in J/C or volts (V).
Sample Problem
• If a 12 V battery does 1200 J of work
transferring charge, how much charge is
transferred?
• ∆V = W/q
• 12 = 1200/q
• q = 100 C
Electric Potential in a Uniform Field
• A uniform field can be made by placing two
large, flat, conducting plates parallel to each
other. One is charged positively and the other
is charged negatively.
• The electric field between the plates is
constant and work is done if the charge is
moved in the direction opposite the electric
field direction.
• ∆V = W/q = Fd/q = (F/q)d = Ed
Sample Problem
• A voltmeter indicates that the electric
potential difference between two plates is
70.0 V. The plates are 0.020 m apart. What
electric field intensity exists between them?
• ∆V = Ed
• 70.0 = E(0.020)
• E= 3500 N/C
Application: Millikan’s Oil Drop
Experiment
• In a Millikan Oil Drop Experiment, a drop has been found to
weigh 2.4 x 10-14 N. The parallel plates are separated by a
distance of 1.2 cm. When the potential difference between
the plates is 450 V, the drop is suspended, motionless. What
is the charge on the oil drop?
• ∆V = Ed
• 450 = E(.012)
• E = 37, 500 N/C
• E = F/q
• 37, 500 = 2.4 x 10-14 N/q
• q = 6.4 x 10-19 C
Application: Millikan’s Oil Drop
Experiment
• How many excess electrons are on the oil
drop?
• 1 electron = 1.6 x 10-19 C
• q = 6.4 x 10-19 C
• 6.4 x 10-19 /1.6 x 10-19 = # of electrons
• # of electrons = 4
Capacitors
• A capacitor is a device used for storing charge.
• Capacitors store energy is the form of separated
charges.
• All capacitors are made up of two conductors that
are separated by an insulator.
• The two conductors have equal and opposite
charges.
• Capacitors are used in electric circuits to store
charge.
• A lightning storm acts as a giant capacitor
arrangement (The cloud is one charged plate and the
Earth is the other. The air acts as the insulator)
Capacitors
• C = q/∆V
• (q is the net charge on each plate; ∆V is the
stored energy obtained by the work done in
separating the charges).
• The unit for capacitance is the C/V or the