Electric Potential in Physics
Phys 102 – Lecture 5
Electric potential
1
Today we will...
•
Learn about the
electric potential
•
Use the principle of superposition
Ex: point charges
•
Represent electric potential with equipotential lines
Relation with electric field
•
Apply these concepts
Ex: Electrocardiogram (ECG)
Phys. 102, Lecture 3, Slide 2
Recall last time
Phys. 102, Lecture 3, Slide 3
h
The electric potential
Units: J/C
V (“volts”)
Electric potential
is a
scalar
(a number) NOT a
vector.
Signs matter!
The electric potential is defined at a
location
in space around
a charge or set of charges
Phys. 102, Lecture 3, Slide 4
Calculation: potential in H atom
r
= 0.53 x 10
–10
m
What is the magnitude of the electric
potential
due to the
proton at the
position
of the electron?
Phys. 102, Lecture 3, Slide 5
Superposition principle
Total potential due to several charges = sum of individual potentials
q
1
q
2
q
3
Ex: what is the electric potential at point
P
due to
q
1
,
q
2
, and
q
3
?
Simple addition, no vectors!
Watch for signs, though!
P
+
–
+
Phys. 102, Lecture 3, Slide 6
Calculation: two charges
Calculate the electric potential at point
P
due to charges
q
1
= +7
μ
C
and
q
2
= –3.5
μ
C
3 m
3 m
4 m
q
2
q
1
P
Phys. 102, Lecture 3, Slide 7
How much work
do you do
bringing a
+2
μ
C
charge from far away to point
P
?
ACT: Electric potential
Phys. 102, Lecture 3, Slide 8
Two charges +2
Q
and –
Q
are placed on the
x
-axis. In which of the three
regions
I
,
II
, or
III
on the
x
-axis can the electric potential be zero?
–Q
+2
Q
I
II
III
A.
I
B.
II
C.
III
D.
II and III
E.
I, II, and III
Equipotential lines
Topographical map
Devils tower, WY
Phys. 102, Lecture 3, Slide 9
Electric potential for a charge
Equipotential lines represent electric potential in space graphically
+
+ Point charge
Phys. 102, Lecture 3, Slide 10
Equipotential & electric field lines
Equipotentials & electric field lines are geometrically related
Phys. 102, Lecture 3, Slide 11
+
3.
Positive charge moves “downhill”
Negative charge moves “uphill”
+
Electric potential for a dipole
+
–
+
–
DEMO
Phys. 102, Lecture 3, Slide 12
ACT: Uniform electric field
Which diagram best represents the equipotential lines corresponding
to a
uniform
E
field pointing to the right?
1
2
3
4
5 V
5
4
3
2
1 V
5 V
1
2
3
4
A.
B.
C.
Phys. 102, Lecture 3, Slide 13
Lect. 4 Checkpoint 1.2
(Revisited)
A
C
B
When a negative charge is moved from A to C, it
moves along an equipotential line
A.
positive work
B.
zero work
C.
negative work
Phys. 102, Lecture 3, Slide 14
ACT: Electric field gradient
A.
B.
C.
Now consider an
E
field that
decreases
going to the right. Which
diagram best represents the equipotential lines?
Large
Small
Phys. 102, Lecture 3, Slide 15
ACT: CheckPoint 2.1
Points A and B lie in an ideal conductor inside a uniform
E
field
A.
Greater than
B.
Equal to
C.
Less than
C
A
B
The electric potential at point A is _____ at point B
Phys. 102, Lecture 3, Slide 16
Electric potential difference
Phys. 102, Lecture 3, Slide 17
Note that the electric field and force depend on electric
potential
difference
Δ
V
, NOT on electric potential
V
itself
Large
Small
Constant
1 V
This will be important starting next lecture with circuits
Vector
Number (“scalar”)
Property of
interacting charges
Property of
point in space
Ex:
Ex:
Ex:
Ex:
F
E
V
U
E
[N]
[J]
[N/C]=[V/m]
[J/C]=[V]
Relationship between F, E, U
E
, V
Phys. 102, Lecture 3, Slide 18
E
points from
high to low
V
Electric potential in biology
Phys. 102, Lecture 3, Slide 19
Ion channels in cell membrane create a charge imbalance
Cells have an electric potential difference across membrane
Cells at rest are
polarized
V
outside
> 0
V
inside
< 0
Electrocardiogram (ECG)
ECG detects electric potential difference from depolarization and
polarization of cardiac tissue
The heart behaves as time-varying electric dipole
V
2
– V
1
Phys. 102, Lecture 3, Slide 20
ACT: Electrocardiogram
Phys. 102, Lecture 3, Slide 21
At a certain time during an ECG you measure a
negative
electric
potential difference
V
2
–
V
1
. Which diagram of the cardiac dipole
could be correct?
V
2
V
1
V
2
V
1
V
2
V
1
A.
B.
C.
Summary of today’s lecture
•
Electric potential
Superposition & point charges
•
Equipotential lines
Relationship with electric field
Ex: Uniform field, non-uniform field, conductor, ECG
Phys. 102, Lecture 3, Slide 22
Today's lecture covers the concept of electric potential, superposition principle, representation with equipotential lines, relation with electric field, and applications like Electrocardiogram (ECG). It explains the definition of electric potential, its scalar nature, and calculation examples involving charges. The superposition principle is discussed in detail for calculating total potential due to multiple charges. An activity challenges understanding of electric potential in different regions on the x-axis.
Download Presentation
Please find below an Image/Link to download the presentation.
The content on the website is provided AS IS for your information and personal use only. It may not be sold, licensed, or shared on other websites without obtaining consent from the author. Download presentation by click this link. If you encounter any issues during the download, it is possible that the publisher has removed the file from their server.
E N D
Presentation Transcript
Phys 102 Lecture 5 Electric potential 1
Today we will... Learn about the electric potential Use the principle of superposition Ex: point charges Represent electric potential with equipotential lines Relation with electric field Apply these concepts Ex: Electrocardiogram (ECG) Phys. 102, Lecture 3, Slide 2
Recall last time Gravitational potential energy Electric potential energy r + + h Height or altitude Electric potential Phys. 102, Lecture 3, Slide 3
The electric potential The electric potential is defined at a location in space around a charge or set of charges EPE of a charge q at position P U Electric potential at position P E V q Charge q Electric potential is 9 V higher at + end than end Units: J/C V ( volts ) + Electric potential is a scalar (a number) NOT a vector. Signs matter! Phys. 102, Lecture 3, Slide 4
Calculation: potential in H atom What is the magnitude of the electric potential due to the proton at the position of the electron? P + r = 0.53 x 10 10 m Phys. 102, Lecture 3, Slide 5
Superposition principle Total potential due to several charges = sum of individual potentials = V V tot Ex: what is the electric potential at point P due to q1, q2, and q3? P Simple addition, no vectors! Watch for signs, though! q1 + q3 + q2 = + + V V V V 1 2 3 tot Phys. 102, Lecture 3, Slide 6
Calculation: two charges Calculate the electric potential at point P due to charges q1 = +7 C and q2 = 3.5 C P 4 m q2 q1 3 m 3 m How much work do you do bringing a +2 C charge from far away to point P? Phys. 102, Lecture 3, Slide 7
ACT: Electric potential Two charges +2Q and Q are placed on the x-axis. In which of the three regions I, II, or III on the x-axis can the electric potential be zero? I II III +2Q Q A. I B. II C. III D. II and III E. I, II, and III Phys. 102, Lecture 3, Slide 8
Equipotential lines Devils tower, WY Topographical map 1. Altitude is constant at every point on this line 2. High (low) value = uphill (downhill) 3. Dense lines = steeper ascent or descent Gravitational potential energy Electric potential energy Height or altitude Electric potential Phys. 102, Lecture 3, Slide 9
Electric potential for a charge Equipotential lines represent electric potential in space graphically kq r = V 1. Electric potential is constant at every point on equipotential line 1V + Point charge 2 3 2. High (low) potential = uphill ( downhill ) 4 + 3. Dense lines = steeper ascent or descent Phys. 102, Lecture 3, Slide 10
Equipotential & electric field lines Equipotentials & electric field lines are geometrically related 1. Electric field points downhill , perpendicular to equipotential lines + 1V 2 3 4 + 2. Dense equipotential lines = large E field 3. Positive charge moves downhill Negative charge moves uphill Phys. 102, Lecture 3, Slide 11
Electric potential for a dipole + 150 100 + 50 0 0 50 100 150 DEMO Phys. 102, Lecture 3, Slide 12
ACT: Uniform electric field Which diagram best represents the equipotential lines corresponding to a uniform E field pointing to the right? E A. B. C. 1 2 3 4 1 2 3 4 5 V 5 V 5 4 3 2 1 V Phys. 102, Lecture 3, Slide 13
Lect. 4 Checkpoint 1.2 (Revisited) C E A B When a negative charge is moved from A to C, it moves along an equipotential line A. positive work B. zero work C. negative work Phys. 102, Lecture 3, Slide 14
ACT: Electric field gradient Now consider an E field that decreases going to the right. Which diagram best represents the equipotential lines? E Large Small A. B. C. Phys. 102, Lecture 3, Slide 15
ACT: CheckPoint 2.1 Points A and B lie in an ideal conductor inside a uniform E field C E A B The electric potential at point A is _____ at point B A. Greater than B. Equal to C. Less than Phys. 102, Lecture 3, Slide 16
Electric potential difference Note that the electric field and force depend on electric potential difference V, NOT on electric potential V itself E 5 Large 5 4 4 1 V 3 3 = E 0 2 2 1 V 1 V E Small E Constant This will be important starting next lecture with circuits Phys. 102, Lecture 3, Slide 17
Relationship between F, E, UE, V Vector Number ( scalar ) F UE [N] [J] q q 1 2 q q r = = 1 2 2 r F k U k Ex: Ex: F r = = cos W E U E V U q E F q E V [J/C]=[V] E [N/C]=[V/m] q q E points from high to low V = = E kr V kr Ex: Ex: 2 Phys. 102, Lecture 3, Slide 18
Electric potential in biology Ion channels in cell membrane create a charge imbalance Cells have an electric potential difference across membrane Cells at rest are polarized Voutside > 0 Vinside < 0 Some cell types (ex: neurons and muscle cells) depolarize when they fire Voutside < 0 Vinside > 0 Phys. 102, Lecture 3, Slide 19
Electrocardiogram (ECG) ECG detects electric potential difference from depolarization and polarization of cardiac tissue + + + + V2 V1 + + + + + + Atrial depolarization Septal depolarization Ventricular depol. V1 V2 The heart behaves as time-varying electric dipole Phys. 102, Lecture 3, Slide 20
ACT: Electrocardiogram At a certain time during an ECG you measure a negative electric potential difference V2 V1. Which diagram of the cardiac dipole could be correct? A. B. C. V1 V2 V1 V1 V2 V2 Phys. 102, Lecture 3, Slide 21
Summary of todays lecture Electric potential Superposition & point charges Equipotential lines Relationship with electric field Ex: Uniform field, non-uniform field, conductor, ECG kq r = V tot Phys. 102, Lecture 3, Slide 22
