AP Phys B
Electrostatics, Circuits, and
Dielectrics and Capacitance
Charge is carried by subatomic particles
• 99% of all charged effects caused by electron
Charging by Conduction
• Physical contact
Charging by Induction
• No physical contact
This law determines the force of attraction or
repulsion between 2 charged objects
• ε0 is a constant – permittivity of free space
• Positive force = repulsive, negative force = attractive
• Remember: force is a vector!
Electric field lines
an electric field.
• More lines =
• Point away from
Electric Fields and conductors
The electric field inside any conductor is
The electric field is always perpendicular
to the surface of a conductor
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 e n c l o s e d
Φ = E A c o s θ
Electric Potential Energy
Electric Potential energy can be determined
Electric potential is defined as the electric
potential energy per unit charge
∆ U q E d= −
= = − ∆ ∆U q V= −
Equipotential lines or surfaces
An equipotential surface is a surface
over which all points have the same
• An equipotential surface must be
perpendicular to the electric field!
Potential due to a point charge
4 0π ε
• Remember: potential is a scalar!
A capacitor is a device that stores electric
The capacitance of an object is defined as:
Capacitance is measured in farads.
Parallel plate capacitors and
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
• Dielectric constant: measures the strength of the
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 Q V=
Electric current is defined as the amount
of charge that flows past a given point in
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.
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
Circuits – emf and terminal
A device that transforms one type of energy
into electrical energy is a “source of
• emf: the potential difference between the terminals of a
battery when there is no current flowing to an external
• A battery has some internal resistance
• The real voltage of a battery is then
V E I r= −
Resistors in series
Current is constant
everywhere in a
R Re q i
V Vt o t a l i
I I It o t a l = = =1 2 . . .
Resistors in parallel
Voltage is constant
everywhere in a
More resistors =
R Re q ii
= ∑I It o t a l i
V V Vt o t a l = = =1 2 . . .
Junction rule: At any junction point, the
total current into the junction has to be
equal to the total current out of the
Loop rule: The sum of changes in
potential around and closed loop is zero.
Every magnet has two poles: north and
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 q v B= s i n θ
F I L B= s i n θ
A moving charge (current) creates a magnetic
• For a long wire, ∆l = 2πr
• Two wires can attract or repel due to this effect.
• A solenoid is a long coil of wire.
B l Ii
e n c l o s e d∆∑ = µ 0
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