Whiteboard Work

Identify similarities and differences between the electric force (Colomb’s law) and the gravitational force (Newton’s gravitational formula).

Announcements

• No pre-lab for next week

• Exam 4 today

Electricity and Magnetism

Underlying a whole lot of phenomena

Outline

• Stationary charges– forces, potential, fields

• Moving charges– current, resistance, circuits

• Magnetism– another effect of moving charges

• Magnetic Induction– Pushing charges with magnetism

Electric Charge

Objectives

• Determine electric force using Coulomb’s Law.

• Explain forces in terms of electric fields.

• Determine energies from electric potential.

Electric Forces Between Objects

always between objects

Coulomb’s Law

F =

k = 8.992 109

C = coulomb (unit of electric charge)

kq1q2

d2

Nm2

C2

Coulomb’s Law

F =

Force is attractive for opposite charges

Force is repulsive for like charges

Proportional to the inverse square of the separation

kq1q2

d2

A hydrogen atom consists of a positive proton and a negative electron. How does the force between the electron and proton change when the electron moves twice as close?

A. The force becomes twice (2) as much.B. The force becomes half (1/2) as much.C. The force remains the same.D. The force becomes four times (4×) as much.E. The force becomes one-fourth (1/4) as much.

Poll Question

Charge Polarization

tells us something about matter

Scenario

A bag contains equal numbers of positive and negative charges. The charges can move around inside the bag, but they cannot leave the bag. The bag is placed near a very large, immobile + charge.

++–

+–

+–

+

–

Quick Question

What sort of force exists between the + charges in the bag and the large + charge?

++–

+–

+–

+

–

A. The + charges are attracted to the charge.

B. The + charges are repelled by the charge.

C. The + charges are neither attracted nor repelled.

Quick Question

What sort of force exists between the – charges in the bag and the large + charge?

++–

+–

+–

+

–

A. The – charges are attracted to the charge.

B. The – charges are repelled by the charge.

C. The – charges are neither attracted nor repelled.

Quick Question

In which direction do the + charges in the bag accelerate due to the large + charge?

++–

+–

+–

+

–

A. Toward the charge.

B. Away from the charge.

C. The + charges will not accelerate.

Quick Question

In which direction do the – charges in the bag accelerate due to the large + charge?

++–

+–

+–

+

–

A. Toward the charge.

B. Away from the charge.

C. The – charges will not accelerate.

Poll Question

After the charges re-distribute, which force to the external + charge will be stronger?

++

–+

–

+

–+

–

A. The attraction to the – charges.

B. The repulsion to the + charges.

C. The attraction and repulsion will exactly cancel.

Poll Question

What sort of force exists between the bag overall and the large + charge?

+

A. The bag is attracted to the charge.

B. The bag is repelled by the charge.

C. The bag is neither attracted nor repelled.

+

–+

–

+

–+

–

Group Poll Question

What sort of force on the bag will exist if the external charge is negative?

–+–

+–

+–

+

–

A. The bag is attracted to the charge.

B. The bag is repelled by the charge.

C. The bag is neither attracted nor repelled.

Electric Fields

around electric charges

Electric Field

• Field E relates the electric force F on an object to its charge q

• Field is a vector

F = qE

Electric field

• Magnitude is the force in N on a +1 C charge

• Direction is the direction of the force exerted on a positive charge

• Vectors point away from positive charges and toward negative charges

• Unit = N/C

Poll Question

A positive charge experiences a force F to the right in an electric field. How does the force change if the field strength doubles?

A. The force becomes 1/4 what it was (F/4).B. The force becomes 1/2 what it was (F/2).C. The force remains the same (F).D. The force becomes 2 what it was (2F).E. The force becomes 4 what it was (4F).F. The force reverses direction (–F).

Fields and Newton’s Third Law

• Field notation is unilateral– Remember that forces are always between

objects

• A charge’s field acts on other charges– Never on itself

Visualizing Fields

• Field vectors

• Field lines

Field Vectors

Board Work

Draw field vectors to describe the electric field of a single positive charge.

+

Field Lines

Field Lines

• Magnitude of the force on a charge is greater where field lines are close together

• Direction of the force is parallel to field lines– Force on a positive charge is along field lines– Force on a negative charge is opposite field

lines

Poll Question

Green arrows are field lines.

Particles A–D have the same charge. Which experiences the greatest force from the field?

A

B

C

D

E. All four forces are equal.

Poll Question

Green arrows are field lines.

Particles A–D have the same charge. Which experiences the greatest force from the field?

A

B

C

D

E. All four forces are equal.

Board Work

Draw field lines to describe the electric field of a single positive charge.

+

Electric Potential

potential energy per charge

Electric Potential

• Field:force as potential:potential energy

• Field is force per charge

• Potential is potential energy per charge

• Unit = J/C = volt = V

Electric Potential

What is the work required to move a charged object through a field?

Work = qE·x = (PE) = q = electric potential = PE/unit charge

xlower higher

Electric Field and Potential

Potential and Field

• Equipotential surfaces are always perpendicular to electric field lines/vectors. Why?

• Potential changes rapidly where field is strong. Why?

It makes sense from the relationships between• Electric field and electric force• Electric potential and electric potential energy• Work and potential energy• Force and work

Reading for Next Time

• Electric current

• Main Ideas– Ohm’s law– Meanings of the quantities in Ohm’s law