AP Phys BTest 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

• Physical contact Charging by Induction

• No physical contact

Coulomb’s Law This law determines the force of attraction or

repulsion between 2 charged objects

• 0 is a constant – permittivity of free space

• Positive force = repulsive, negative force = attractive• Remember: force is a vector!

FQ Q

rq 1

4 0

1 22

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

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

Q enclosed

0

EA cos

Electric Potential Energy Electric Potential energy can be determined

using mechanics

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

U qEd

VUq

Wq

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

VQr

1

4 0

• Remember: potential is a scalar!

Capacitance A capacitor is a device that stores electric

charge. The capacitance of an object is defined as:

Capacitance is measured in farads.

CQV

Parallel plate capacitors and dielectrics For a parallel plate capacitor (two conducting

plates with a vacuum between the plates)

Often, an insulator known as a dielectric is placed between the plates to enhance capacitance• Dielectric constant: measures the strength of the

dielectric

CAd

0

Capacitors and energy A charged capacitor stores an amount of

electric energy given by

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

U QV12

2

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.

RVI

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.

RLA

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 circuitR Req i

i

V Vto ta l ii

I I Ito ta l 1 2 . . .

Resistors in parallel Current additive Voltage is constant

everywhere in a series circuit

More resistors = smaller equivalent resistance

1 1R Req ii

I Ito ta l ii

V V Vto ta l 1 2 . . .

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

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

F qvB s in

F ILB s in

Right hand rule

Ampere’s Law A moving charge (current) creates a magnetic

field.

• For a long wire, l = 2r• Two wires can attract or repel due to this effect.• A solenoid is a long coil of wire.

B l Iii

enclosed 0

Faraday’s Law A changing magnetic field induced an emf.

• 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.

E Nt