1.3 Electric Force
Coulombs Law describes the electric force between charged objects.
Size:
Coulombs constant k = 9x109 Nm2/C2
Direction:
Opposite charges attract along line r.
Like charges repel along line r.
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Example:
Consider the ground state of a H-1
1
Motion of Charged Particles in E-Fields
A charged particle of mass m moving in a region of electric field experiences an
acceleration with a size of
If the electric field is uniform in this region then the acceleration is constant and
the equations of m
1.4 Electric Field
Symbol
E
mks units
[N/C]
A charged object with charge qo produces an electric field vector at every point in
space except at its position. This object exerts an electrical force on another
charged object with charge q. This force is giv
1.1: Review of Vectors
Review your vectors! You should know how to
convert from polar form to component form and vice versa
add and subtract vectors
multiply vectors by scalars
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Example:
Find the resultant vector R = r2 3r1 where r1 = 10 m, 45 and r2 = 2
Voltage (Potential)
Symbol
V
mks units
[Volts = V]
A charged object with charge qo produces a voltage at every point in space except
at its position. This object shares a potential energy with another charge q. This
energy is given by
where V is the volta
Continuous Charge Distributions
If point P is near a large charged object, then to find the electric field at P you chop
up the object into many point charges. You find the electric field due to each point
charge and sum up all these field vectors.
Exampl
1
Combinations of Resistors
Resistors in parallel share the same voltage difference.
The equivalent resistance of two resistors in parallel is
This equation can be solved for the equivalent resistance to give
-Resistors in series have the same current flo
Symbol
I, i
mks units
[Amperes = Amps = A = C/s]
The current is the rate that charge flows from one point to another.
By convention, current flows in the direction that positive charge would travel in a
circuit. (In practice, it is the flow of electrons i
A capacitor is a device that can store opposite charge (+Q and Q) on two different
surfaces when a voltage difference (V) is applied between the surfaces. The
capacitance (C) of the capacitor determines how much charge can be stored for a
given voltage di
Positive charges speed up when going from high to low voltage. They slow down
when going from low to high voltage.
Negative charges speed up when going from low to high voltage. They slow down
when going from high to low voltage.
Using the previous equati
A. Charged Particles
A moving charged particle creates a magnetic field vector at every point in space
except at its position.
Symbol for Magnetic Field
B
mks units
[Tesla = T = N/(Am)]
other common unit
[Gauss = G] [1 G = 10-4 T]
This magnetic field exer
Application 1: Synchrotron (Particle Accelerator)
Accelerate charge particles with an electric force as they travel a circular path with
a fixed radius r. The magnetic field necessary to keep them moving in that circle is
found from the above force equati
AC Generators
A generator consists of a coil that is rotated in a magnetic field. A time-varying
voltage difference that regularly changes polarity is produced of the form
VM = amplitude of the voltage [V]
= angular frequency of the rotation [rad/s]
Note
Biot-Savart Law
A moving charge produces a magnetic field at a point P given by
A. Straight Wire
Field at a point due to the current in a straight wire segment
Size:
Direction: Field Right Hand Rule #1 (Field RHR #1)
1. Place thumb along current I so that
Faraday's Law
The magnetic flux through a loop of wire is
B = magnetic field penetrating loop [T]
A = area of loop [m2]
= angle between field vector and a vector perpendicular to the plane
of the loop
mks units of flux
[T-m2 = Weber = Wb]
If we define th
1
D. Solenoid (Coil)
Field at a point on the central axis of a solenoid with length and N turns
Size:
Direction: Field Right Hand Rule #2 (Field RHR #2)
1. Follow I around coil with fingers.
2. Thumb gives direction of B along axis.
Special Case: Long sol
Wave a disturbance in a medium that propagates
Transverse wave - the disturbance is perpendicular to the propagation
direction
(e.g., wave on a string)
Longitudinal wave the disturbance is parallel to the propagation direction
(e.g., sound wave)
1-D Wave
Converting from sound level to intensity:
= sound level [decibel = dB]
I = intensity in [W/m2]
Some sources of sound can be approximated as point sources. A point source
sends out a wave uniformly in all directions. The energy is spread out uniformly
acr
T = period = time for one oscillation or cycle [s]
f = 1 / T = frequency = number of cycles per time [cycles/s =
Hz]
= 2 / T = 2f
[rad/s]
The sign between kx and t determines the direction the wave travels along the xaxis.
+ wave travels to left (in the d
A inductor is a device that develops a voltage difference between the ends of the
device when the current (I) through it changes. The inductance (L) of the inductor
determines the size of the induced voltage (V).
If the time interval approaches zero, then