General Physics (PHY 2140). Lecture 5. Electrostatics Electrical energy potential difference and electric potential potential energy of charged conductors Capacitance and capacitors. http://www.physics.wayne.edu/~apetrov/PHY2140/. Chapter 16. Lightning Review. Last lecture:
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Lecture 5
http://www.physics.wayne.edu/~apetrov/PHY2140/
Chapter 16
The total electric potential at some point P due to several point charges is the algebraic sum of the electric potentials due to the individual charges.
q2
q1
r
P
A
Three ions, Na+, Na+, and Cl, located such, that they form corners of an equilateral triangle of side 2 nm in water. What is the electric potential energy of one of the Na+ ions?
Cl
?
Na+
Na+
… but that’s not all!
The electron volt is defined as the energy that electron (or proton) gains when accelerating through a potential difference of 1 V
1 eV = 1.60´1019 C·V = 1.60´1019 J
Vab=1 V
In the Bohr model of a hydrogen atom, the electron, if it is in the ground state, orbits the proton at a distance of r = 5.29´1011 m. Find the ionization energy of the atom, i.e. the energy required to remove the electron from the atom.
Note that the Bohr model, the idea of electrons as tiny balls orbiting the nucleus, is not a very good model of the atom. A better picture is one in which the electron is spread out around the nucleus in a cloud of varying density; however, the Bohr model does give the right answer for the ionization energy
The ionization energy equals to the total energy of the electronproton system,
Given:
r = 5.292 x 1011 m
me = 9.11´1031 kg
mp = 1.67´1027 kg
e = 1.60´1019 C
Find:
E=?
with
The velocity of e can be found by analyzing the force on the electron. This force is the Coulomb force; because the electron travels in a circular orbit, the acceleration will be the centripetal acceleration:
or
or
Thus, total energy is
a
+Q
b
Q
Capacitor for use in highperformance audio systems.



+
e0= 8.85´1012 C2/N·m2
A
+Q
d
A
Q
Solution:
Given:
DV=10,000 V
A = 2.00 m2
d = 5.00 mm
Find:
C=?
Q=?
Since we are dealing with the parallelplate capacitor, the capacitance can be found as
Once the capacitance is known, the charge can be found from the definition of a capacitance via charge and potential difference:
C5
C3
C2
C4
16.8 Combinations of capacitorsC2
C1
C3
C1
+Q1
C2
+Q2
V=Vab
Q1
Q2
b
a. Parallel combinationConnecting a battery to the parallel combination of capacitors is equivalent to introducing the same potential difference for both capacitors,
A total charge transferred to the system from the battery is the sum of charges of the two capacitors,
By definition,
Thus, Ceq would be
(parallel combination)
A 3 mF capacitor and a 6 mF capacitor are connected in parallel across an 18 V battery. Determine the equivalent capacitance and total charge deposited.
C1
+Q1
C2
+Q2
V=Vab
Q1
Q2
b
A 3 mF capacitor and a 6 mF capacitor are connected in parallel across an 18 V battery. Determine the equivalent capacitance and total charge deposited.
Given:
V = 18 V
C1= 3 mF
C2= 6 mF
Find:
Ceq=?
Q=?
First determine equivalent capacitance of C1 and C2:
Next, determine the charge
+Q1
C1
Q1
V=Vab
c
+Q2
C2
Q2
b
b. Series combinationConnecting a battery to the serial combination of capacitors is equivalent to introducing the same charge for both capacitors,
A voltage induced in the system from the battery is the sum of potential differences across the individual capacitors,
By definition,
Thus, Ceq would be
(series combination)
A 3 mF capacitor and a 6 mF capacitor are connected in series across an 18 V battery. Determine the equivalent capacitance.
+Q1
C1
Q1
V=Vab
c
+Q2
C2
Q2
b
A 3 mF capacitor and a 6 mF capacitor are connected in series across an 18 V battery. Determine the equivalent capacitance and total charge deposited.
Given:
V = 18 V
C1= 3 mF
C2= 6 mF
Find:
Ceq=?
Q=?
First determine equivalent capacitance of C1 and C2:
Next, determine the charge