1. Physics 16/21 Electromagnetism
Equipotential Surface & Potential Gradient
MARLON FLORES SACEDON
Reminder: 4th Long exam: April 2, 2017 Sunday (2:00-4:00 PM)

2. Equipotential surface
In electrostatics, the work done to move a charge from any point on the equipotential surface to any other point on the equipotential surface is zero since they are at the same potential. Furthermore, equipotential surfaces are always perpendicular to the net electric field lines passing through it.

3. Equipotential
Topographic map

4. Equipotential
In electrostatics, the work done to move a charge from any point on the equipotential surface to any other point on the equipotential surface is zero since they are at the same potential. Furthermore, equipotential surfaces are always perpendicular to the net electric field lines passing through it.

5. Potential gradient
Definition of potential gradient. : the vector that represents the rate at which a potential changes with position in a specified direction; specifically : the rate of change with height of the atmospheric electric potential.
then
𝑉 𝑎 − 𝑉 𝑏 = 𝑎 𝑏 𝐸 ∙𝑑 𝑙
−𝑑𝑉= 𝐸 𝑥 𝑑𝑥
𝐸 𝑥 =− 𝑑𝑉 𝑑𝑥 𝑦,𝑧 𝑐𝑜𝑛𝑠𝑡𝑎𝑛𝑡
𝑉 𝑎 − 𝑉 𝑏 = 𝑏 𝑎 𝑑𝑉 =− 𝑎 𝑏 𝑑𝑉
then
− 𝑎 𝑏 𝑑𝑉 = 𝑎 𝑏 𝐸 ∙𝑑 𝑙
−𝑑𝑉= 𝐸 ∙𝑑 𝑙
𝐸 = 𝐸 𝑥 𝑖 + 𝐸 𝑦 𝑗 + 𝐸 𝑧 𝑘
𝑑 𝑙 = 𝑖 𝑑𝑥+ 𝑗 𝑑𝑦+ 𝑘 𝑑𝑧
−𝑑𝑉= 𝐸 𝑥 𝑑𝑥+ 𝐸 𝑦 𝑑𝑦+ 𝐸 𝑧 𝑑𝑧
Suppose the displacement is parallel to x-axis
𝑑 𝑦 = 𝑑 𝑧 =0

6. Potential gradient
Definition of potential gradient. : the vector that represents the rate at which a potential changes with position in a specified direction; specifically : the rate of change with height of the atmospheric electric potential.

7. Alternative solution
𝑟= 𝑥 2 + 𝑦 2 + 𝑧 2

9. Assignment

10. Assignment

11. Assignment

12. Assignment

13. Assignment

14. Assignment

15. Assignment

16. Assignment

17. Assignment

18. Answers to odd numbers

19. eNd