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Chapter 17
Electric Charge and Electric Field
Two kinds of charges: positive and
negative
• Two charges of the same kind
REPEL each other
• Two charges of different kinds
ATTRACT each other
Coulomb’s Law
• The magnitude F of the force that each of
two point charges q1 and q2 exerts on each
other when they are separated by a distance
r is directly proportional to the product of
the two charges and inversely proportional
to the distance squared
F = k |q1q2|/r2
Additive forces
r12
q1
r23
q2
r13
q3
ELECTRIC FIELD
GAUSS’s LAW
The total flux ΦE coming out of any closed
surface is proportional to the total electric
charge Qencl inside the volume
surrounded by this surface.
ΦE = Qencl / ɛo
Ɛo = 8.854x10-12C2/(N.m2)
Chapter 18
Electric Potential and Capacitance
ELECTRIC POTENTIAL ENERGY
Electric potential energy is between two
charges (q and q’ ) separated by a distance
r and is defined as:
PE = kqq’/r
Electric potential energy is a scalar and has
units of Joule (J).
When there are more than 2 charges, the total
potential energy is the sum of the energy
associated with each pair of charges
• In the gravitational case, the change in the
potential energy associated with an object
with mass m when moved from the surface
to a height h is
mgh
Similarly, the electric potential energy
associated with a charge q in a field E is:
qEd
When the charge is moved a distance d along
or opposite direction of the field
ELECTRIC POTENTIAL or VOLTAGE
• A charge Q creates an electric field around it.
Similarly, this charge will create an electric potential
V around it, commonly called voltage
It is a scalar and is defined as:
V = kQ/r
The unit for electric potential is the Volt (V).
Consequently, when a charge q is placed at a
distance r from Q, the electric potential energy
between the two charges would be:
U = qV
ELECTRIC POTENTIAL and ELECTRIC FIELD
• For parallel plates separated by a distance d
and a potential difference between them V
the field between the plates is then:
E= V/d
Or
V=Ed
DEFINITION
• The CAPACITANCE C of a capacitor is the
ratio of the magnitude of the charge Q on
either conductor (plate) to the magnitude of
the potential Vab between the conductors
(plates):
C =Q/Vab
The SI unit of capacitance is FARAD
(1farad = 1C/1V)
CAPACITANCE FOR PARALLEL PLATES
• If the capacitor is made of parallel plates
with surface area A and a separation d
between the plates, the capacitance is:
C = ɛ0A/d
Capacitors are often joined
Capacitors are often joined II –
Figures 18.22
Electric Field Energy in a Capacitor
• One of the applications of the capacitor is
to store energy (analogous to the potential
energy stored in a spring)
Ucapacitor = (1/2) CV2
Chapter 19
Current, Resistance, and
Directed-Current Circuits
Current defined
Unit: 1coulomb/second = 1 ampere = 1A
Resistance and Ohm’s Law
• When the potential difference V between the
two ends of a conductor is proportional to
the current I passing through the conductor,
the ratio (V)/(I) is called the resistance of
the conductor :
R = V/I
The SI unit for resistance is the ohm and it is
represented by the Greek letter Ω
1Ω = 1V/A
Resistivity
• The resistance is the property of a given conductor
and it depends on its length L and cross- section
area A
R = ρ L/A
L
ρ characterizes the conduction properties of the
material
Power in Electric Circuit
The power P is defined as
P = VabI
The unit for power is the watt
1W = 1J/s
Power for a pure resistor:
For a pure (single) resistor, we have:
P=VabI
Since V= RI
P = RI2 or P = V2ab/R
Connections in series
Req = R1 + R2 + R3
SAME CURRENT
DIFFERENT POTENTIAL
Connections
in parallel
1/Req = 1/R1 + 1/R2 + 1/R3
SAME POTENTIAL
DIFFERENT CURRENT
Just after two identical point charges are released
when they are a distance D apart in outer space,
they have an acceleration a.
If you release them from a distance D/2 instead,
their acceleration will be
A. a/4
B. 4a
C. 2a
D. a/2
Just after two identical point charges are released
when they are a distance D apart in outer space,
they have an acceleration a.
If you release them from a distance D/2 nstead,
their acceleration will be
A. a/4
B. 4a
C. 2a
F = k |q1q2|/D2
a = F/m
4a
D. a/2
If the electric field is E at a distance d from a point charge,
its magnitude will be 2E at a distance:
A. d/4
B. d/2
C. d/
2
D. d
2
E. 2d
If the electric field is E at a distance d from a point charge,
its magnitude will be 2E at a distance:
A. d/4
B. d/2
C. d/
2
E = k q/d2
C
D. d
2
E. 2d
Two unequal point charges are separated as shown in the figure
The electric field due to this combination of charges can be zero
A. only in region 1.
B. only in region 2.
C. only in region 3.
D. in both regions 1 and 3.
Two unequal point charges are separated as shown in the figure
The electric field due to this combination of charges can be zero
A. only in region 1.
B. only in region 2.
C. only in region 3.
D. in both regions 1 and 3.
Two protons close to each other are released from rest and
are completely free to move.
After being released (there may be more than one correct
choice),
A. their speeds gradually decrease to zero as they move
apart.
B. their speeds gradually increase as they move apart.
C. their accelerations gradually decrease to zero as they
move apart.
D. their accelerations gradually increase as they move
apart.
Two protons close to each other are released from rest and
are completely free to move.
After being released (there may be more than one correct
choice),
A. their speeds gradually decrease to zero as they move
apart.
B. their speeds gradually increase as they move apart.
C. their accelerations gradually decrease to zero as they
move apart.
D. their accelerations gradually increase as they move
apart.
• A spherical balloon contains a charge +Q uniformly
distributed over its surface. When it has a diameter D ,
the electric field at its surface has magnitude E .
If the balloon is now blown up to twice this diameter without
changing the charge, the electric field at its surface is
A. 4E
B. 2E
C.E/4
D. E/2
• A spherical balloon contains a charge +Q uniformly
distributed over its surface. When it has a diameter D ,
the electric field at its surface has magnitude E .
If the balloon is now blown up to twice this diameter without
changing the charge, the electric field at its surface is
A. 4E
B. 2E
C.E/4
D. E/2
An electron is moving horizontally in a laboratory when a
uniform electric field is suddenly turned on. This field points
vertically downward (in the plane of the paper).
Which of the paths shown will the electron follow, assuming
that gravity can be neglected?
An electron is moving horizontally in a laboratory when a
uniform electric field is suddenly turned on. This field points
vertically downward (in the plane of the paper).
Which of the paths shown will the electron follow, assuming
that gravity can be neglected?
In the figure below, point P is equidistant from both point
charges.
•
•
•
•
•
At that point (there may be more than one correct choice),
A.the electric field points directly to the right.
B. the electric field is zero.
C. the potential (relative to infinity) is zero.
D. the potential (relative to infinity) points upward.
In the figure below, point P is equidistant from both point
charges.
• At that point (there may be more than one correct choice),
• A.the electric field points directly to the right.
• B. the electric field is zero.
• C. the potential (relative to infinity) is zero.
• D. the potential (relative to infinity) points upward.
V is a scalar and is defined as:
V = kQ/r
For the capacitor network shown in the figure below
a constant potential difference of 50.0 V is maintained
across points a and b by a battery.
Which of the following statements about this network is correct?
A. The 10 μF and 20 μF capacitors have equal charges.
B. The charge on the 20 μF capacitor is twice the charge on the 10 μF capacitor.
C. The potential difference across the 10 μF capacitor is the same as the potentia
difference across the 20 μF capacitor.
D. The equivalent capacitance of the network is 60 μF .
For the capacitor network shown in the figure below
a constant potential difference of 50.0 V is maintained
across points a and b by a battery.
Which of the following statements about this network is correct?
A. The 10 μF and 20 μF capacitors have equal charges.
B. The charge on the 20 μF capacitor is twice the charge on the 10 μF capacitor.
C. The potential difference across the 10 μF capacitor is the same as the potentia
difference across the 20 μF capacitor.
D. The equivalent capacitance of the network is 60 μF .