PHYS 2135Engineering Physics II

Course Information• Canvas• Intro Video• Course Handbook• Syllabus• Instructors• Lectures• Homework• Old Exams

No labs this week

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

-

n +

- +

++-

Charged Insulators and Conductors

The force is proportional to the product of the charges.

++

+++

++

++

Charged Conductors

Examples:

Electric Charge

Charge is quantized• Discrete amounts are multiples of

• Protons have positive charge,

• Neutrons have no net charge

• Electrons have negative charge, C

++n

n

-

(Atom is not drawn to scale.)

+

n

-

Coulomb’s Law

The force on one charge due to another charge.

q1 q2

Coulomb’s Law

The force on one charge due to another charge.

Force due to q1 acting on q2.

q1 q2

Coulomb’s Law

The force on one charge due to another charge.

Constant that depends on system of units. Found on OSE sheet.

q1 q2

NmC

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.

q1 q2

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.

q1 q2

Coulomb’s Law

The force on one charge due to another charge.

Direction vector is away from q1.

q1 q2

Coulomb’s Law

The force on one charge due to another charge.

Newton’s Third Law

q1 q2

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?

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.

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

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).

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).

• 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.)

- +

h

d

r- r+

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

- +

h

d

r- r+

-

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

- +

y

d

r- r+

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

- +

y

d

r- r+

Should we be concerned about the z-direction?

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

- - - - - - - - -

+ + + + + + + + +

+

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

- - - - - - - - -

+ + + + + + + + +

+

Was it reasonable to ignore gravity?