Understanding Electric Potential in Physics

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.

• Electric Potential
• Physics
• Superposition Principle
• Equipotential Lines
• Electric Field

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1. Phys 102 Lecture 5 Electric potential 1

2. 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

3. Recall last time Gravitational potential energy Electric potential energy r + + h Height or altitude Electric potential Phys. 102, Lecture 3, Slide 3

4. 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

5. 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

6. 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

7. 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

8. 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

9. 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

10. 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

11. 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

12. Electric potential for a dipole + 150 100 + 50 0 0 50 100 150 DEMO Phys. 102, Lecture 3, Slide 12

13. 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

14. 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

15. 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

16. 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

17. 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

18. 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

19. 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

20. 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

21. 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

22. 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