Post on 19-Mar-2020
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Chapter 19: Electric Potential &
Potential Energy
Brent Royuk Phys-112
Concordia University
Terminology • Two Different Quantities:
– Electric Potential and Electric Potential Energy • Electric Potential = Voltage • Note: We will start by considering a point
charge, section 18-3.
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Electric Potential Energy • Consider two point charges separated by a
distance r. The energy of this system is
• To derive this, you need to integrate work using Coulomb’s Law.
• Potential energies are always defined relatively. Where is U = 0 for this system?
• What is negative energy? • This is a scalar quantity. • The Superposition Principle applies. • We are most often interested in changes and
differences, rather than absolutes.
€
U =kqoq
r
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Electric Potential • Definition:
– This is called the electric potential (which shouldn’t be confused with electric potential energy), the potential, or the voltage.
– Remember: potential is energy per charge. • Units
– In MKS, energy/charge = Joule/Coulomb = 1 volt (V)
• In everyday life, what’s relevant about this infinity stuff? Nothing, really. – Potentials tend to be differences. One
commonly chosen zero: the earth.
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V =Uqo
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Comparisons • An Analogy
– Coulomb Force --> Electric Field (Force per charge), as
– Electric Potential Energy --> Electric Potential (Energy per charge)
• How is electric potential energy similar to gravitational potential energy?
• Potential in this chapter compared to future chapters.
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Electric Potential • For a point charge,
€
V =Uqo
=kqqo
rqo
=kqr
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Electric Potential Examples • A battery-powered lantern is switched on for 5.0
minutes. During this time, electrons with total charge -8.0 x 102 C flow through the lamp; 9600 J of electric potential energy is converted to light and heat. Through what potential difference do the electrons move?
• Find the energy given to an electron accelerated through a potential difference of 50 V. – a) The electron volt (eV)
• An electron is brought to a spot that is 12 cm from a point charge of –2.5 µC. As the electron is repelled away, to what speed will it finally accelerate?
• Find the electric field and potential at the center of a square for positive and negative charges. – What do positive and negative voltages mean? – E-field lines point in the direction of decreasing V.
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Electric Potential Examples • How much work is required to assemble the
charge configuration below?
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1 4
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Electric Potential Examples • Consider the three charges shown in the figure
below. How much work must be done to move the +2.7 mC charge to infinity?
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Potential in a Uniform Field • Let’s let an electric field do some work
as we move a test-charge against the field:
• The work done by the field is: W = -qoEd
• Assuming we start at the U = 0 point, we get U = -W = qoEd
• Signs? See next slide. • Using the definition of the potential we
get: V = Ed
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Potential in a Uniform Field • Sign considerations: • Work done by the field is negative, which
makes the potential energy positive (useful). – Compare with gravity:
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Potential in a Uniform Field
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Potential in a Uniform Field • Example: A uniform field is
established by connecting the plates of a parallel-plate capacitor to a 12-V battery. a) If the plates are separated by 0.75 cm, what is the magnitude of the electric field in the capacitor? b) A charge of +6.24 µC moves from the positive plate to the negative plate. How much does its electric potential energy change?
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Equipotential Surfaces • An equipotential surface has the
same potential at every point on the surface.
• Equipotential surfaces are perpendicular to electric field lines. – The electric field is the gradient of
the equipotential surfaces.
• How are equipotential lines oriented to the surface of a conductor?
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Equipotential Surfaces
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Equipotential Surfaces • Comparative examples:
– Isobars on a weather map. – Elevation lines on a topographic map.
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Capacitors • A plate capacitor • It takes energy to charge the plates
– Easy at first, then harder
• Q = CV – C is the capacitance – Bigger C means more charge per volt, bigger charge
storage device – 1 farad (F) = 1 coulomb/volt
• – εo = 8.85 x 10-12 C2/Nm2 (permittivity of free space) – Connect with k
• What area plate separated by a gap of 0.10 mm would create a capacitance of 1.0 F?
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C =εoAd
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Capacitors in Circuits • Series
– Charge is same on all capacitors – Voltage drops across the capacitors – So V = V1 + V2 + V3 +... – Since V = Q/C, – Therefore:
• Parallel – The voltage is the same across all capacitors.
Different amounts of charge collect on each capacitor
– Q = Q1 + Q2 + Q3 +... – Q = CV, so CeqV = C1V + C2V + C3V + ... – Generally,
€
QCeq
=QC1
+QC2
+QC3
+ ...
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1Ceq
=1C1
+1C2
+1C3
+ ...
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Ceq = C1 + C2 + C3 + ...
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Dielectrics • In real life, capacitor plates are not
naked, the gap is filled with a dielectric material – Dielectrics are insulators. – Keeps plates separated, easier to build. – Also increases the capacitance
• The dielectric constant – Isolated capacitor: insert dielectric, E is
reduced by 1/κ • κ = the dielectric constant • C = κCo
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Dielectrics
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Electrical Energy Storage • Graph V vs. q:
• What is the area under the curve?
V
Q
Slope = 1/C
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U =12
QV =Q2
2C=
12
CV 2
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Electrical Energy Storage • A defibrillator is used to deliver 200 J of
energy to a patient’s heart by charging a bank of capacitors to 750 volts. What is the capacitance of the defibrillator?
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