The following is some equations and functions that are essential to Physics 1110. They are taken directly from the following Physics book:
where F is the force of interaction; 
; 
and 
are point charges; and
r is the distance between the two point charges.
where ;
q' is the test charge;
is the electrical force; and
is the electrical field. The direction of the
electrical field and force are the same.
where p is the
electric
dipole moment, E is the electric field, and 
is the
angle between the vectors 
and 
.
Another way to write this equation is as
a cross product: 
where is the electric field vector; dA is the slice of
area that is going through; and is the angle
between the perpendicular and dA. Therefore 
is the surface area through which flows.
Another way to express the electric flux is as
follows: 
where q is
a point charge and 
is a universal constant. This
eqation only applies to the electric flux in a sphere. (pg. 640
Section 23-2)
where 
is the total charge enclosed
by the
surface. Thus this integral must always be over a closed
surface.
where 
is the surface charge density of the plates and the plates are
oppositely charged.
where U is the electric potential energy; and q' is a
test charge a distance r from the charge q.
When there are many test charges, the electric
potential energy can be expressed as follows: 
.
where V is the potential.
where 
is the potential difference and equals the
work done by an external force.
The expression is read as
" is the negative of the gradient of V." This can also be
expressed as components:
where C is capacitance
and is measured in Farads and 
is the potential
difference between the conductors.
where A is the
area of the capacitor and d is the distance between the
capacitors.
This equation is for capacitors that
are in series.
This
equation is
for capacitors that are in parallel.
To calculate the potential energy U of a charged
capacitor, one can calculate the work required to charge
it.
Thus, defining the potential energy of an uncharged capcaitor as zero:
where I is the current which
is the net charge flow dQ through an area in the time dt.
where J is the current
density; A is the cross-section area; n is the
concentration of particles; and 
is the magnitude of the
drift velocity.
where 
is
resistivity, J is
the current density, and E is the electric field.
where is
resistivity; L
is the length of the conductor; and A is the cross-sectional
area of the conductor.
(resistors in
series)
(resistors in parallel)
The following is the Junction Rule: 
(any
junction)
The following is the Loop Rule: 
(any
closed loop)
The force on a charge
moving with velocity 
in a magnetic field 
.
where 
are
infitesimal segments of a conductor and 
is the force on
each segment in the magnetic field, .
where A is the area of
the loop, I is the current flowing through it, and is the
angle the loop is from the perpendicular.
where 
is the
magnetic
moment and is equal to IA.
where R is a unit vector equal to 
,
r being
the distance from the charge. Also, is the perticle's
velocity.
where r is the
radial distance of the magnetic field away from the center of the
conductor.
where N is the number of circular loops a is the radius of the
circular conductor, and x is the distance to a point.
where
is the algebraic sum of the currents enclosed or linked
by the integration path.
The angular velocity of the perticle is as follows:
where
R is the radius of the circular path.
Thus, the induced
emf in a circuit equals the negative of the time rate of
change of
magnetic flux through the circuit.
where L is the length of a given
rod.
For any two points a and b the motional emf in the
direction from b to a is 
q
