Physics 212 Lecture 6, Physics 212 Lecture 6, Slide Slide 1 Physics 212 Physics 212 Lecture 6 Lecture 6 Today's Concept: Today's Concept: Electric Potential Electric Potential Defined in terms of Path Integral of Defined in terms of Path Integral of Electric Field Electric Field
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Physics 212 Lecture 6, Slide 1 Physics 212 Lecture 6 Today's Concept: Electric Potential Defined in terms of Path Integral of Electric Field.
Physics 212 Lecture 6, Slide 3 Your Comments 05 “.” “I'm pretty sure my head just exploded. Just... everywhere.” “help! i need somebody help! not just anybody help! you know i need someone HELLPP" “ ” “That last one was a doozy. Equipotential lines seem like they hold the key to something, but I don't know what yet.” “Do we have to be able to use/do problems with gradients?” “Are we going to differentiate the electric potential in three dimensions in order to get the electric field?” “The calculations with the spherical insulator were hard to follow. And I understand simple ideas, but I hope that the lecture helps me understand more fully.” Electric potential is related to energy – a key aspect of E’nM. We will use electric potential extensively when we talk about circuits. We really only need to know about derivatives (partial derivatives in a few cases). See example at end of class. Not too bad. After discussion today, I understand Gauss's Law!
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Defined in terms of Path Integral of Electric FieldDefined in terms of Path Integral of Electric Field
Physics 212 Lecture 6Physics 212 Lecture 6
MusicWho is the Artist?Who is the Artist?
A)A) John PrineJohn PrineB)B) Little FeatLittle FeatC)C) Taj MahalTaj MahalD)D) Ry CooderRy CooderE)E) Los LobosLos Lobos
Why?Why?
Last time did Buena Vista Social Club (Cuba)Last time did Buena Vista Social Club (Cuba)Ry Cooder was the guy who brought them to our attention in this countryRy Cooder was the guy who brought them to our attention in this country
Also, this album is great…. Also, this album is great….
““I'm pretty sure my head just exploded. Just... everywhere.”.”
“help! i need somebody help! not just anybody help! you know i need someone HELLPP"““That last one was a doozy. Equipotential lines seem like they hold the key to something, but I don't know what yet.””
“Do we have to be able to use/do problems with gradients?”“Are we going to differentiate the electric potential in three dimensions in order to get the electric field?”
“The calculations with the spherical insulator were hard to follow. And I understand simple ideas, but I hope that the lecture helps me understand more fully.”
Electric potentialElectric potential is related to energy – a key aspect of E’nM. is related to energy – a key aspect of E’nM.We will use We will use electric potentialelectric potential extensively when we talk about circuits. extensively when we talk about circuits.
We really only need to know about derivatives (partial derivatives in a We really only need to know about derivatives (partial derivatives in a few cases).few cases).
See example at end of class.See example at end of class.
Not too bad. After discussion today, I understand Gauss's Law!
Electric Potential from E fieldElectric Potential from E field• Consider the three points A, B, and C located in a region of constant electric field as shown.
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• What is the sign of VAC = VC - VA ? (A) VAC < 0 (B) VAC = 0 (C) VAC > 0
When the electric field is zero in a certain region, the electric potential is surely zero in that region. However it is not certain that the electric potential is zero elsewhere.
Suppose the electric field is zero in a certain region of space. Which of the following statements best describes the electric potential in this region of space?
A. The electric potential is zero everywhere in this regionB. The electric potential is zero at at least one point in this regionC. The electric potential is constant everywhere in this regionD. There is not enough information to distinguish which of the answers is correct
The potential is the integral of E dx. If E is zero then when you integrate you will just get a constant.
“The field lines are dense at points A, B, and C, which indicates that the field is strong. However the lines are very spread out at D, indicating that the field is weakest there..“
The field-line representation of the E-field in a certain region of space is shown below. The dashed lines represent equipotential lines.
At which point in space is the E-field weakest?A. B. C. D.
ABCD“The equipotential is weaker in the region between c and d than in the region from a to b.“
“The work is directly proportional to the distance between two charges. The distance between C and D is further away from that of A and B.”
“The charge would have to cross the same number of equipotential lines regardless, so the change in potential energy is the same and therefore the work is the same.“
The field-line representation of the E-field in a certain region of space is shown below. The dashed lines represent equipotential lines.
Compare the work done moving a negative charge from A to B and from C to D. Which move requires more work?A. From A to B B. From C to DC. The same D. Cannot determine without performing calculation
• A and C are on the same equipotential • B and D are on the same equipotential• Therefore the potential difference between A and B is the SAME as the potential between C and D
The field-line representation of the E-field in a certain region of space is shown below. The dashed lines represent equipotential lines.
Compare the work done moving a negative charge from A to B and from C to D. Which move requires more work?A. From A to B B. From C to DC. The same D. Cannot determine without performing calculation
“because the electric field is constant, moving the charge from A to D would require the most work since it has the furthest displacement.”
“The electric field is greater at point D than B.“
“B and D are on the same equipotential line.“
The field-line representation of the E-field in a certain region of space is shown below. The dashed lines represent equipotential lines.
Now compare the work done moving a negative charge from A to B and from A to D. Which move requires more work?A. From A to B B. From A to DC. The same D. Cannot determine without performing calculation
Calculation for PotentialCalculation for PotentialPoint charge q at center of concentric conducting spherical shells of radii a1, a2, a3, and a4. The inner shell is uncharged, but the outer shell carries charge Q.
What is V as a function of r?+q+q
metal
metal
+Q+Q
a1
a2
a3a4
• Conceptual Analysis: – Charges q and Q will create an E field throughout space
0
( )r
r
V r E d
–
• Strategic Analysis: – Spherical symmetry: Use Gauss’ Law to calculate E