Electric Potential
Electrostatic Potential Energy and
Potential Difference
The electrostatic force is
conservative – potential
energy can be defined
Change in electric potential
energy is negative of work
done by electric force:
Electrostatic Potential Energy and
Potential Difference
Electric potential is defined as potential
energy per unit charge:
Unit of electric potential: the volt (V).
1 V = I J/C.
Electrostatic Potential Energy and
Potential Difference
Only changes in potential can be measured,
allowing free assignment of V = 0.
Electrostatic Potential Energy and
Potential Difference
Analogy between gravitational and electrical
potential energy:
Equipotential Lines
An equipotential is a line or
surface over which the
potential is constant.
Electric field lines are
perpendicular to
equipotentials.
The surface of a conductor is
an equipotential.
Equipotential Lines
The Electron Volt, a Unit of Energy
One electron volt (eV) is the energy gained by
an electron moving through a potential
difference of one volt.
Electric Potential Due to Point Charges
The electric potential due to a point charge
can be derived:
Electric Potential Due to Point Charges
These plots show the
potential due to (a)
positive and (b) negative
charge.
Electric Potential Due to Point Charges
Using potentials instead of fields can make
solving problems much easier – potential is a
scalar quantity, whereas the field is a vector.
Capacitance
A capacitor consists of two conductors
that are close but not touching. A
capacitor has the ability to store electric
charge.
Capacitance
Parallel-plate capacitor connected to battery. (b)
is a circuit diagram.
Capacitance
When a capacitor is connected to a battery, the
charge on its plates is proportional to the
voltage:
The quantity C is called the capacitance.
Unit of capacitance: the farad (F)
1 F = 1 C/V
Capacitance
The capacitance does not depend on the
voltage; it is a function of the geometry and
materials of the capacitor.
For a parallel-plate capacitor:
A parallel–plate capacitor has a capacitance Co.
A second parallel–plate capacitor has plates with
twice the area and twice the separation. The
capacitance of the second capacitor is most
nearly
(A) ¼Co
(B) ½Co
(C) Co (D) 2Co (E) 4Co
A parallel–plate capacitor has a capacitance Co.
A second parallel–plate capacitor has plates with
twice the area and twice the separation. The
capacitance of the second capacitor is most
nearly
(A) ¼Co
(B) ½Co
(C) Co (D) 2Co (E) 4Co
Two square parallel–plate capacitors of
capacitances C1 and C2 have the dimensions
shown in the diagrams above. The ratio of C1 to
C2 is
(A) 1 to 4
(B) 1 to 2
(C) 1 to 1 (D) 2 to 1
(E) 4 to 1
Two square parallel–plate capacitors of
capacitances C1 and C2 have the dimensions
shown in the diagrams above. The ratio of C1 to
C2 is
(A) 1 to 4
(B) 1 to 2
(C) 1 to 1 (D) 2 to 1
(E) 4 to 1
Dielectrics
A dielectric is an insulator, and is
characterized by a dielectric constant K.
Capacitance of a parallel-plate capacitor filled
with dielectric:
Dielectrics
Dielectric strength is the
maximum field a
dielectric can experience
without breaking down.
Dielectrics
The molecules in a dielectric tend to become
oriented in a way that reduces the external
field.
Dielectrics
This means that the electric field within the
dielectric is less than it would be in air,
allowing more charge to be stored for the
same potential.
A sheet of mica is inserted between the plates of
an isolated charged parallel–plate capacitor.
Which of the following statements is true?
(A)The capacitance decreases.
(B) The potential difference across the capacitor
decreases.
(C) The energy of the capacitor does not change.
(D) The charge on the capacitor plates decreases
(E) The electric field between the capacitor plates
increases.
A sheet of mica is inserted between the plates of
an isolated charged parallel–plate capacitor.
Which of the following statements is true?
(A)The capacitance decreases.
(B) The potential difference across the capacitor
decreases.
(C) The energy of the capacitor does not change.
(D) The charge on the capacitor plates decreases
(E) The electric field between the capacitor plates
increases.
Since the capacitor is isolated, Q remains constant. Filling the place
with oil (a dielectric) will increase the capacitance, causing the
potential (V = Q/C) to decrease.
Which of the following capacitors, each of which
has plates of area A, would store the most
charge on the top plate for a given potential
difference V?
Which of the following capacitors, each of which
has plates of area A, would store the most
charge on the top plate for a given potential
difference V?
The capacitor with the
largest capacitance will
store the most charge.
C = 0A/d where glass
> air and vacuum so E
Storage of Electric Energy
A charged capacitor stores electric energy;
the energy stored is equal to the work done
to charge the capacitor.
A 20 μF parallel–plate capacitor is fully charged
to 30 V. The energy stored in the capacitor is
most nearly
(A)9 × 103 J (B) 9 × 10–3 J (C) 6 × 10–4 J
(D) 2 × 10–4 J
(E) 2 × 10–7 J
A 20 μF parallel–plate capacitor is fully charged
to 30 V. The energy stored in the capacitor is
most nearly
(A)9 × 103 J (B) 9 × 10–3 J (C) 6 × 10–4 J
(D) 2 × 10–4 J
(E) 2 × 10–7 J
UC = ½ CV2
A potential difference V is maintained between
two large, parallel conducting plates. An electron
starts from rest on the surface of one plate and
accelerates toward the other. Its speed as it
reaches the second plate is proportional to
(A) 1/V (B)
(C) √V (D) V (E) V2
A potential difference V is maintained between
two large, parallel conducting plates. An electron
starts from rest on the surface of one plate and
accelerates toward the other. Its speed as it
reaches the second plate is proportional to
(A) 1/V (B)
(C) √V (D) V (E) V2
W = K = qV and K = ½ mv2