VAC = Vm sin(wt)
For this kind of AC voltage, we can determine the amplitude (max) of the
voltage (Vm= NBAw) . But since the average of sine is zero, how do we
treat the average?
What is usually important is the power delivered by the electric circuit.
For safety, we like to have rather low voltages in the house.
For economy, since Plost = I2R, we like to have low currents (which means
high voltages) in our transmission lines.
We can have both if we use transformers located in our neighborhoods!
We have already done programs on Gravitational Deflection (trajectories PHYS 201, Vol. 1, #6) and Electric Deflection (cathode ray tube, Vol. 3, #3).
Since we have introduced a third basic force, magnetism, we will try to do a
Magnetic Deflection program
To start, we must consider the magnetic field and how it exerts a magnetic
force on our particle: F = q v B sin(qvB) with the force direction
perpendicular to both v and B.
Any velocity component parallel to B will not have a force associated with it.
From the mechanical analogy, this should be like having a mass with air
resistance. If we have a constant force (like gravity), the object will
accelerate up to a terminal speed (due to force of air resistance increasing
up to the point where it balances
We have made an electric generator that can generate electrical energy.
But according to the Law of Conservation of Energy, we can only convert
energy from one form into another. In the case of the electric generator,
where does this energy come from?
DV = D[ (N B A cos(qBA) ] / Dt
The above formula, Faradays Law, is for determining the amount of
voltage generated. But what is the direction of that voltage (i.e., what
direction will it try to drive a current)?
The answer is Lenzs Law: the direction of
A typical roulette wheel is initially spun at 18 radians per second and takes 10
seconds to stop. Its diameter is 80 cm. Find the following.
(a) initial tangential speed of a point on the rim of the wheel
(b) initial frequency of the wheel in rev
We start from the definition of voltage: V = PE/q (or PE = qV). But since
the voltage across an inductor is related to the current change, we might
express q in terms of I:
I = dq/dt, or dq = I dt. Therefore, we have:
Estored = S qi Vi = V dq = V I dt and
There is a similar effect for a capacitor in an AC circuit. For a capacitor,
since VC = q/C, VC will be small if C is big and/or if is big (causing little q to
accumulate in the short time).
A more detailed calculation for reactance gives XC = 1/(C), and
r = mv/qB
If we make the speed too small, the radius will not be big enough so that
the particle will not go far enough to reach the target.
A minimum size circle would have to have a diameter equal to the distance
the target is from the firing point:
1. At a particular instant a particle of mass m A = 5 mg and charge of qA = 5
Coul is located at the origin. A second particle of mass m b = 2 mg and
charge of qB = -6 Coul is located at that same instant at a position (-5 m, +3
m) relative to the origin.
You are to finish designing a mass spectrometer to measure the mass of
some unknown atoms. A sketch of the spectrometer is shown below. The atoms
are first singly ionized by removing one electron from each atom. They are then
accelerated between Plates 1
Design lenses out of glass with an index of refraction of 1.5 with the following
characteristics. To design a lens, you must specify the radii of curvature of the two
a) a positive lens with f = +10 cm, shaped like a "football"
b) a positive len
5. Consider two charges (same as for problem S-4): qA has a charge of 5
nCoul and is located at (5 m, 3 m); qB has a charge of -4 nCoul and is
located at (7 m, -2 m).
a) What is the electric potential at the origin due to q A alone?
b) What is the electri
A typical optical fiber has a cylindrical core with an index of refraction of 1.62
wrapped by a cladding jacket whose index of refraction is 1.52. The diameter of
the core is 50 m (microns). Light traveling in air is launched into one end of the
a) Design an electric motor that operates at 3000 rpm and delivers an average
power of 186.5 Watts (one-fourth of a horsepower). Do this by specifying the
number of coil windings, the area of the winding core, the current that the motor
draws, and the siz
3.5 Magnesium fluoride (n = 1.38) is often used as an antireflecting coating on
lenses. Find the minimum thickness necessary to use on a glass lens with n =
1.5 so that the loss of light due to reflection is minimized. Since white light is
comprised of a
One of the natural radioactive decay series is the uranium series which begins with
U and ends with 206Pb. The half-life for the complete decay sequence is 4.47x109
years. The first decay in the series is the emission of an alpha particle by the
4.1 You are sitting in your room doing physics homework. Your skin temperature
is 95F (a typical skin temperature). Let's say that your skin surface area is
12000 cm2 and that you radiate as a perfect blackbody.
a) At what wavelength does your thermal rad
Design a compound microscope with a total magnifying power of 500x. The
distance between the objective and eyepiece lenses must be between 12 cm and 16
cm. Tell me your design by specifying the following quantities:
total magnification (Mtot)