1. Physics 133 Electromagnetism
Electric Potential
MARLON FLORES SACEDON

2. ∙ ∙ electric potential - What is Electric Potential?
An electric potential, the amount of work needed to move a unit charge from a reference point to a specific point against an electric field.
From definition of electric field, 𝐸= 𝑘𝑄 𝑟 2 , substitute in Eq.3… becomes,
From: 𝑊=𝐹𝑆𝑐𝑜𝑠𝜃
𝑊=𝐹𝑟
𝑉= 𝑘𝑄 𝑟 2 𝑟
𝑈=𝐹𝑟 𝐸
𝑈=𝑞𝐸𝑟
Def’n of Electric potential energy
Eq.1
𝑉= 𝑘𝑄 𝑟
Electric potential for a single source charge
𝑉= 𝑈 𝑞 ∙ 𝑏
Eq.2 𝑟
Eq.2 is the definition of electric potential. Where: 𝑈 is electric potential energy, 𝑞 is unit charge, & 𝑉 is electric potential.
𝑉=𝑘 𝑄 1 𝑟 𝑄 2 𝑟 2 +… 𝑄 𝑛 𝑟 𝑛
Electric potential for multiple source charge 𝐹
Substitute Eq.1 in Eq.2 ∙ 𝑎
𝑉= 𝑞𝐸𝑟 𝑞 +𝑞 - 𝑄
𝑉=𝐸𝑟
Eq.3

3. ∙ ∙ electric potential - Units:
If the charge 𝑞 equals the magnitude 𝑒 of the electron charge, 1.602𝑥 10 −19 𝐶, and the potential difference is 𝑉 𝑎𝑏 =1 𝑉, the change in energy is called Electron Volt.
MKS: 1 𝐽𝑜𝑢𝑙𝑒 𝑐𝑜𝑢𝑙 =1 𝐽 𝐶 =1 𝑣𝑜𝑙𝑡=1 𝑉
CGS: 1 𝑒𝑟𝑔 𝑠𝑡𝑎𝑡𝐶 =1 𝑠𝑡𝑎𝑡𝑉 𝐸
1 𝑉=300 𝑠𝑡𝑎𝑡𝑉
1 eV=1.60𝑥 10 −19 𝐽 𝐹
+e=1.602𝑥 10 −19 𝐶 ∙ 𝑏 +𝑞 𝑟 ∙ 𝑎 - 𝑄

4. electric potential
Problem 1: An electric dipole consists of point charges 𝑞 1 =+12𝑛𝐶 and 𝑞 2 =−12𝑛𝐶 placed 10.0 cm apart. Compute the electric potentials at points 𝑎, 𝑏, and 𝑐.
From the def’n of electric potential
𝑉 𝑏 =9𝑥 𝑁. 𝑚 2 𝐶 𝑥 10 −9 𝐶 4 𝑥10 −2 𝑚 + −12 𝑥10 −9 𝐶 14 𝑥10 −2 𝑚
𝑉=𝑘 𝑄 1 𝑟 𝑄 2 𝑟 2 +… 𝑄 𝑛 𝑟 𝑛
𝑉 𝑏 =1, 𝑉
𝑉 𝑎 =𝑘 𝑞 1 𝑟 𝑞 2 𝑟 2
𝑉 𝑐 =9𝑥 𝑁. 𝑚 2 𝐶 𝑥 10 −9 𝐶 13 𝑥10 −2 𝑚 + −12 𝑥10 −9 𝐶 13 𝑥10 −2 𝑚
𝑉 𝑎 =9𝑥 𝑁. 𝑚 2 𝐶 𝑛𝐶 6𝑐𝑚 + −12𝑛𝐶 4𝑐𝑚
𝑉 𝑐 =0 𝑉
𝑉 𝑎 =9𝑥 𝑁. 𝑚 2 𝐶 𝑥 10 −9 𝐶 6 𝑥10 −2 𝑚 + −12 𝑥10 −9 𝐶 4 𝑥10 −2 𝑚
=9𝑥 𝑁. 𝑚 2 𝐶 2 −1𝑥 10 −7 𝐶 𝑚
𝑉 𝑎 =−900 𝑁.𝑚 𝐶 =−900 𝐽 𝐶 =−900 𝑣𝑜𝑙𝑡𝑠=−900 𝑉

5. potential Difference ∙ ∙ What is potential difference?
The potential difference between two points is defined as: Potential difference between two points in a circuit is the work done in moving unit charge from one point to the other. The units for potential difference are Joules per coulomb, or volts. (1 𝑣𝑜𝑙𝑡 = 1 𝐽𝑜𝑢𝑙𝑒/𝑐𝑜𝑢𝑙𝑜𝑚𝑏).
Potential difference is often time called Voltage or Electromotive force
𝑊=−∆𝑈
work done by electric potential
𝑊 𝑎𝑏 =− 𝑈 𝑏 − 𝑈 𝑎
𝑊 𝑎𝑏 =− 𝑈 𝑏 + 𝑈 𝑎
High potential
Low potential ∙ a
𝑊 𝑎𝑏 = 𝑈 𝑎 − 𝑈 𝑏 𝑞
𝑊 𝑎𝑏 = 𝑞𝑉 𝑎 − 𝑞𝑉 𝑏
How much work done by the moving charge?
𝑊 𝑎𝑏 = 𝑞 𝑉 𝑎 − 𝑉 𝑏 ∙ b
𝑊 𝑎𝑏 𝑞 = 𝑉 𝑎 − 𝑉 𝑏
𝐹𝑟 𝑞 = 𝑉 𝑎 − 𝑉 𝑏
𝑞𝐸𝑟 𝑞 = 𝑉 𝑎 − 𝑉 𝑏
𝐸𝑟= 𝑉 𝑎 − 𝑉 𝑏
Note: 𝑉 𝑎 − 𝑉 𝑏 is potential difference or voltage

6. potential Difference ∙ ∙ What is potential difference?
The potential difference between two points is defined as: Potential difference between two points in a circuit is the work done in moving unit charge from one point to the other. The units for potential difference are Joules per coulomb, or volts. (1 𝑣𝑜𝑙𝑡 = 1 𝐽𝑜𝑢𝑙𝑒/𝑐𝑜𝑢𝑙𝑜𝑚𝑏).
Potential difference is often time called Voltage or Electromotive force
𝑊=−∆𝑈
work done by electric potential
𝑊 𝑎𝑏 =− 𝑈 𝑏 − 𝑈 𝑎
𝑊 𝑎𝑏 =− 𝑈 𝑏 + 𝑈 𝑎
High potential
Low potential ∙ a
𝑊 𝑎𝑏 = 𝑈 𝑎 − 𝑈 𝑏 𝑞
𝑊 𝑎𝑏 = 𝑞𝑉 𝑎 − 𝑞𝑉 𝑏
How much work done by the moving charge?
𝑊 𝑎𝑏 = 𝑞 𝑉 𝑎 − 𝑉 𝑏 ∙ b
𝑊 𝑎𝑏 𝑞 = 𝑉 𝑎 − 𝑉 𝑏
𝐹𝑟 𝑞 = 𝑉 𝑎 − 𝑉 𝑏
𝑞𝐸𝑟 𝑞 = 𝑉 𝑎 − 𝑉 𝑏
𝐸𝑟= 𝑉 𝑎 − 𝑉 𝑏
Note: 𝑉 𝑎 − 𝑉 𝑏 is potential difference or voltage

7. potential Difference
Problem: In figure, a dust particle with mass 𝑚=5.0𝑥 10 −9 𝑘𝑔=5.0 𝜇𝑔 and charge 𝑞=2.0 𝑛𝐶 starts from rest and moves in a straight line from point 𝑎 to point 𝑏. What is its speed 𝑣 at point 𝑏.
The force acts on dust particle is a conservative force. So, from conservation of energy…
𝐸 𝑎 = 𝐸 𝑏
𝑉 𝑎 =9𝑥 𝑁. 𝑚 2 𝑘𝑔 𝑥 10 −9 𝐶 0.01𝑚 + −3𝑥 10 −9 𝐶 0.02𝑚 =1350 𝑉
𝐾 𝑎 + 𝑈 𝑎 = 𝐾 𝑏 + 𝑈 𝑏
0+ 𝑞𝑉 𝑎 = 1 2 𝑚 𝑣 2 + 𝑞𝑉 𝑏
𝑉 𝑏 =9𝑥 𝑁. 𝑚 2 𝑘𝑔 𝑥 10 −9 𝐶 0.02𝑚 + −3𝑥 10 −9 𝐶 0.01𝑚 =−1350 𝑉
1 2 𝑚 𝑣 2 = 𝑞𝑉 𝑎 − 𝑞𝑉 𝑏
𝑉 𝑎 − 𝑉 𝑏 =1350− −1350 =2700 𝑉
𝑣= 2𝑞 𝑉 𝑎 − 𝑉 𝑏 𝑚
𝑣= 2 2𝑥 10 −9 𝐶 𝑉 5𝑥 10 −9 𝑘𝑔 =46 𝑚 𝑠

8. General problems
1. A charge of 20𝑥 10 −8 𝐶 is 20 𝑐𝑚 from another charge of 180𝑥 10 −8 𝐶
a) Find the force between the two
b) What is the potential at the point which is exactly midway between the two
c) What is the electric field intensity at the same point.

9. General problems 2.

10. General problems 4.

11. General problems

12. General problems

13. General problems

14. General problems

15. General problems

16. eNd