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: