1. Engineering Physics II
Fall 2018
Instructor:
Dr. Jim Musser
Physics 122
Course Information:
Canvas and Course Website
Begin with Course Handbook and Syllabus

2. Engineering Physics II
Fall 2018
Lecture
Get the big picture.
Learn as much as you can.
Recitation and Homework
Fill in the gaps.
Put it all together.
Practice.
Lab
Apply concepts in physical situations.

3. Engineering Physics II Fall 2018 Textbook:
Sears & Zemansky’s University Physics
Any recent edition (latest is 14th)
by Young and Freedman

4. PHYS 2135
Office Hours
Time set aside by the instructor to answer student questions
Times and Location:
11:00 a.m. – 12:00 p.m., Monday and Wednesday
Physics 122
Other times by appointment
Recitation Instructors are primary contacts

5. Important Information
Disability Support Services (accommodation letters)
Testing Center

6. Property of matter (similar to mass)
Electric Charge
What is charge?
Property of matter (similar to mass)
Describes how strongly objects interact electrically
Two kinds of charge
Labeled positive and negative
Like charges repel
Unlike (opposite) charges attract
Law of Conservation of Charge:
Net amount of charge does not change in any process - + - + - +

7. Charged Insulators and Conductors+ - - + + - +

8. Charged Insulators and Conductors
The force is proportional to the product of the charges. + + + ++ ++ ++

9. Charged Conductors
Examples:

10. Discrete amounts are multiples of 𝑒=1.6× 10 −19 C
Electric Charge
Charge is quantized
Discrete amounts are multiples of 𝑒=1.6× 10 −19 C
Protons have positive charge,
+𝑒= +1.6× 10 −19 C
Neutrons have no net charge
Electrons have negative charge,
−𝑒=−1.6× 10 −19 C + - n - + n
(Atom is not drawn to scale.) n +

11. Coulomb’s Law
The force on one charge due to another charge.
𝑟 12
𝑟 12
𝐹 12 q1 q2
𝐹 12 =𝑘 𝑞 1 𝑞 2 𝑟 𝑟 12

12. Force due to q1 acting on q2.
Coulomb’s Law
The force on one charge due to another charge.
Force due to q1 acting on q2.
𝐹 12
𝑟 12
𝑟 12 q1 q2
𝐹 12 =𝑘 𝑞 1 𝑞 2 𝑟 𝑟 12

13. Constant that depends on system of units. Found on OSE sheet.
Coulomb’s Law
The force on one charge due to another charge.
Constant that depends on system of units. Found on OSE sheet.
𝑟 12
𝑟 12
𝐹 12 q1 q2
𝐹 12 =𝑘 𝑞 1 𝑞 2 𝑟 𝑟 12
𝑘=9× N m 2 C 2

14. The force on one charge due to another charge.
Coulomb’s Law
The force on one charge due to another charge.
Amount and sign of each charge.
Like (unlike) charges → Force is away from (towards) q1.
𝑟 12
𝐹 12
𝑟 12 q1 q2
𝐹 12 =𝑘 𝑞 1 𝑞 2 𝑟 𝑟 12

15. The force on one charge due to another charge.
Coulomb’s Law
The force on one charge due to another charge.
Square of distance between charges.
Force decreases rapidly as if charges are moved apart.
𝐹 12
𝑟 12
𝑟 12 q1 q2
𝐹 12 =𝑘 𝑞 1 𝑞 2 𝑟 𝑟 12

16. Direction vector is away from q1.
Coulomb’s Law
The force on one charge due to another charge.
Direction vector is away from q1.
𝑟 12
𝐹 12
𝑟 12 q1 q2
𝐹 12 =𝑘 𝑞 1 𝑞 2 𝑟 𝑟 12

17. Coulomb’s Law
The force on one charge due to another charge.
Newton’s Third Law
𝐹 21
𝑟 12
𝐹 12
𝑟 12
𝑟 21 q1
𝑟 21 q2
𝐹 12 =𝑘 𝑞 1 𝑞 2 𝑟 𝑟 12 =−𝑘 𝑞 2 𝑞 1 𝑟 𝑟 21 =− 𝐹 21

18. Example: Three charges are arranged as follows
Example: Three charges are arranged as follows. Q1 = q0 is at (0, d), Q2 = q0 is at the origin and Q3 = -2q0 is at (2d, 0). q0 is positive. Determine the force acting on Q1.

19. Example: Three charges are arranged as follows
Example: Three charges are arranged as follows. Q1 = q0 is at (0, d), Q2 = q0 is at the origin and Q3 = -2q0 is at (2d, 0). q0 is positive. Determine the force acting on Q1.
If Q1 were released from the given position, what would be its initial direction of acceleration?
Would the acceleration of Q1 remain constant as it moved?
If not, how would the acceleration change?

20. Electric Field
What would be the force on a charge if it were located here or anywhere?

21. Electric Field
Gravitational Field Analogy
Consider a smoothly varying surface near the earth.
Imagine placing a ball anywhere on the surface.
Direction of force would be downhill.
Strength of force would be proportional to steepness.
The field exists everywhere.
Force per mass that would be experienced by an object at any location.

22. Electric Field
Consider space around a charge or a set of charges.
Imagine placing another charge anywhere in the space.
Electric field gives the direction and relative strength of the force.
The field exists everywhere.
Force per charge that would be experienced by an object at any location.

23. Electric Field
Force per charge
𝐸 = 𝐹 𝑞
𝐹 01 =𝑘 𝑞 0 𝑞 1 𝑟 𝑟 01
𝐸 =𝑘 𝑞 0 𝑟 2 𝑟

24. Electric Field
Force on a particular charge at a particular location (due to another charge elsewhere).
Force per charge that would exist at all locations (due to a charge elsewhere).
𝐹 01 =𝑘 𝑞 0 𝑞 1 𝑟 𝑟 01
𝐸 =𝑘 𝑞 0 𝑟 2 𝑟

25. Electric Field
Force on a particular charge at a particular location (due to another charge elsewhere).
Force per charge that would exist at all locations (due to a charge elsewhere).
𝐹 01 =𝑘 𝑞 0 𝑞 1 𝑟 𝑟 01
𝐸 =𝑘 𝑞 0 𝑟 2 𝑟
Does it make sense to calculate the force of a charge on itself?
Does it make sense to calculate the electric field due to a charge at the location of the charge?

26. Example: An electron and positron (charge +e) are arranged as shown.
a. Determine the electric field at P. (P is equidistant to the two charges.) r- r+ h - + d

27. Example: An electron and positron (charge +e) are arranged as shown.
b. What would be the force on an electron placed at P? - r- r+ h - + d

28. Example: An electron and positron (charge +e) are arranged as shown.
c. Determine the electric field everywhere equidistant from the two charges. r- r+ y - + d

29. Example: An electron and positron (charge +e) are arranged as shown.
c. Determine the electric field everywhere equidistant from the two charges. r- r+ y - + d
Should we be concerned about the z-direction?

30. Examples: A proton enters a region with a uniform electric field
Examples: A proton enters a region with a uniform electric field. Describe the proton’s motion as a function of time.
𝑣 0 + 𝐸

31. Was it reasonable to ignore gravity?
Examples: A proton enters a region with a uniform electric field. Describe the proton’s motion as a function of time.
𝑣 0 + 𝐸
Was it reasonable to ignore gravity?