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

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.

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

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

Important Information Disability Support Services (accommodation letters) http://dss.mst.edu/ Testing Center http://testcenter.mst.edu/

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 - + - + - +

Charged Insulators and Conductors + - - + + - +

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

Charged Conductors Examples:

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 +

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 12 2 𝑟 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 12 2 𝑟 12

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 12 2 𝑟 12 𝑘=9× 10 9 N m 2 C 2

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 12 2 𝑟 12

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 12 2 𝑟 12

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 12 2 𝑟 12

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 12 2 𝑟 12 =−𝑘 𝑞 2 𝑞 1 𝑟 21 2 𝑟 21 =− 𝐹 21

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.

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?

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

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.

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.

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

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 01 2 𝑟 01 𝐸 =𝑘 𝑞 0 𝑟 2 𝑟

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 01 2 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?

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

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

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

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?

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 + + + + + + + + +

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?