Introductory Physics Volume Two

184 Hints A
6.6 Use a phasor diagram to draw Kirchhoff’s loop rule, then find the
frequency that minimizes the effective impedance of the RLC combination.
6.8 Use Faraday’s law. Assume that the magnetic field decreases at
a constant rate over the 20 ms that it goes from 1.6 T to zero, that is
dB/dt = (−1.6T)/(20ms).
6.10 Since the field strength decreases as you move further from the
wire you will need to do an integral in order to compute the magnetic
flux.
6.11 Use Ampere’s Law.
6.13 Consider that Q = ∫ Idt and I = V/R = E/R.
7.2 Start from x = A cos φ.
7.3 Take a look at the diagram of the oscillator that shows the phase
angle at different points in the cycle. For the last part remember that
v = dx/dt and consider the quantity v/x.
7.4 Recall that the phase is φ = ωt + φ 0 so that ∆φ = ω∆t. Then
consider by how much the phase must change in order for the oscillator
to complete one cycle.
7.8 First compute the phase difference. Remember that φ 1 = −kr 1
and φ 2 = −kr 2 . Next use the addition of two waves theorem.
7.9 The collection of points with the same ∆r will form a continuous
line, just like the collection of points that are all 5cm from a single
point makes a circle or radius 5 cm.
7.10 Treat the two holes as two sources.
7.11 The phase of each path is now −kr plus the reflection phase
shift.
7.12 Find the distance from the lower speaker to the point P as a
function of the distance d.
7.15 The path difference occurs in air.
7.16 Use the far field approximation to find the path difference.
7.18 Use the trig identities in the appendix.
7.19 There is a path difference, d sin θ, on both sides of the screen.
7.22 The air gap between the plates will be wedge shaped, because
the thickness of the air gap increases as you move toward the wire,
there will be an increasing phase difference between the two reflected
beams. This leads to the fringes.
7.24 As the slit gets narrower the angle of the first minima increases.
There is a limit to the increase.