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AP Phys B Test Review Electrostatics, Circuits, and Magnetism 4/29/2008

Overview  Electrostatics  Electric

Potential  Dielectrics and Capacitance  Electric Current  DC Circuits  Magnetism

Electrostatics  Charge

is carried by subatomic particles (protons, electrons)

• 99% of all charged effects caused by electron transfer

 Charging

by Conduction

 Charging

by Induction

• Physical contact

• No physical contact

Coulomb’s Law 

This law determines the force of attraction or repulsion between 2 charged objects

1 Q 1Q 2 Fq = 4 πε 0 r 2 • • •

ε0 is a constant – permittivity of free space Positive force = repulsive, negative force = attractive Remember: force is a vector!

Electric field lines A

visual representation of an electric field.

• More lines = •

stringer force Point away from positive, toward negative.

Electric Fields and conductors  The

electric field inside any conductor is

zero  The electric field is always perpendicular to the surface of a conductor

Gauss’ Law 

Electric Flux: The amount of an electric field passing through an area

Φ = E A cosθ 

Gauss’ Law: The total electric flux passing through a closed surface is proportional to the charged enclosed in that surface.

Q e n c lo s e d Φ = ε0

Electric Potential Energy 

Electric Potential energy can be determined using mechanics

∆U = −qEd



Electric potential is defined as the electric potential energy per unit charge

U W V = = − q q

∆U = −q∆V

Equipotential lines or surfaces  An

equipotential surface is a surface over which all points have the same potential.

• An equipotential surface must be

perpendicular to the electric field!

Potential due to a point charge • Remember: potential is a scalar!

1 Q V = 4 πε0 r

Capacitance 



A capacitor is a device that stores electric charge. The capacitance of an object is defined as:

Q C = V



Capacitance is measured in farads.

Parallel plate capacitors and dielectrics 

For a parallel plate capacitor (two conducting plates with a vacuum between the plates)

ε0 A C = d 

Often, an insulator known as a dielectric is placed between the plates to enhance capacitance

•

Dielectric constant: measures the strength of the dielectric

Capacitors and energy 

A charged capacitor stores an amount of electric energy given by

1 U = Q V 2 2

•

This energy can be thought of as stored in the electric field between the plates.

Electric Current  Electric

current is defined as the amount of charge that flows past a given point in a second

Ohm’s Law 

Ohm’s Law related the resistance of an object to the decrease in electric potential across a point and the current flowing through that point.

V R = I

Electric Resistance 

Electric resistance is the innate ability of a material to inhibit the passage of electrons.

• •

Measured in ohms. Given by the resistivity as well as the geometry of the object.

L R = ρ A

Circuits – emf and terminal voltage 

A device that transforms one type of energy into electrical energy is a “source of electromotive force”

• • •

emf: the potential difference between the terminals of a battery when there is no current flowing to an external source. A battery has some internal resistance The real voltage of a battery is then

V = E − Ir

Resistors in series 



Voltage and resistance are additive Current is constant everywhere in a series circuit R eq =

V to ta l

∑ Ri i = ∑ Vi i

I to ta l = I 1 = I 2 = . . .

Resistors in parallel  



Current additive Voltage is constant everywhere in a series circuit More resistors = smaller equivalent resistance I to ta l =

∑ i

Ii

V to ta l = V 1 = V 2 = . . .

1

1 = ∑ R eq Ri i

Complex Circuits

Kirchhoff’s rules  Junction

rule: At any junction point, the total current into the junction has to be equal to the total current out of the junction.  Loop rule: The sum of changes in potential around and closed loop is zero.

Kirchhoff’s Rules

Magnetism  Every

magnet has two poles: north and

south  Magnetic field & magnetic field lines: analogous to electric field

• Direction: points north to south

 Electric

current (moving charge) produces a magnetic field!

Force due to magnetic fields 

The force on a charged particle moving through a magnetic field

F = q v B s in θ 

The force in a current carrying wire immersed in a magnetic field

F = IL B s in θ

Right hand rule

Ampere’s Law 

A moving charge (current) creates a magnetic field.

∑ • • •

i

B ∆ li = µ 0 I e n c lo s e d For a long wire, ∆l = 2πr Two wires can attract or repel due to this effect. A solenoid is a long coil of wire.

Faraday’s Law 

A changing magnetic field induced an emf.

∆Φ E = − N ∆t

• •

A current produced by an induced emf moves in a direction such that its magnetic field opposes the original change in flux (Lenz’s Law) A coil rotating in a magnetic field is a good example of this.